Can something have more sugar per 100g than the percentage of sugar that's in it?

Looking up Shreddies, I found this site. It lists, in the ingredients

Whole Grain Wheat (96%), Sugar, Invert Sugar Syrup, Barley Malt Extract, Salt, Molasses, Vitamins and Minerals (Niacin, Iron, Pantothenic Acid, Folic Acid, Vitamin B6, Riboflavin)

There is no percentage for the sugar in the ingredients list.

And the nutritional information says

Carbohydrate 70g of which sugars 13g

If that's where your confusion comes from, then it is simply that you didn't realize the different meanings of the word "sugar".

Chemically, sugars are a class of molecules with a roughly similar structure, most of which taste similar. For a cook or food technologist, "sugar" is any ingredient that constist of one or many of these molecules and can be used to sweeten food. And finally, in everyday language, "sugar" without any further qualifications is exactly one of these products, namely white crystal sugar, that consists of the molecule sucrose only.

In the ingredients list, the second ingredient uses this third meaning of the word sugar - they have put less white table sugar than whole grain into the cereal (making the white sugar amount at most 4%). The nutrition label uses the first meaning - it sums together all chemical sugars in the cereal. And it is normal for even unprocessed whole grain to contain some of those - this being a cereal, and a malted one at that, it has more of them. So, part of your "whole grain" ingredient is made up of (chemically) sugars, as well as the "sugar" ingredient, the "invert sugar syrup" ingredient, possibly the "barley malt extract" (pure malt is quite a bit of sugar), and the "molasses" ingredient. Together, the weight of chemical sugars is 13% of the cereal.

I suspect that 96g of whole grain goes into the recipe for 100g, along with 13g of sugar and some salt, vitamins, and flavouring ingredients. At that point there's at least 109g. Then it's formed and cooked, driving off at least 9g of water, getting down to 100g.

I don't know in what form the whole wheat is added, but whole wheat flour has more than 20% moisture as sold, so it's easy to drive some of this off. This isn't water as an ingredient, this is moisture in the grain.

The wording gives it away. They don't say there's 96g of whole wheat in 100g of finished product. They say they started with 96g. That 96g has reduced to no more than 87g by the time it goes into the box. This is more obvious on ketchup - the bottle in my fridge says "prepared with 157g of tomatoes per 100g of product"

A couple things for clarification. First, some have speculated that the percentages do not refer to true percentages. Assuming this is UK labeling, as in the link rumtscho noted, the 96% per UK regulations must refer to the amount per 100 grams of the product by weight (from 96.2 grams of whole wheat). It turns out I was wrong about this in some cases. See NOTE added at the end of this answer. Canadian versions note that Shreddies are 94.9% "whole grain wheat."

That seemingly leaves only about 4-5% of other ingredients for sugar. As rumtscho points out, "sugar" here can include all sorts of different chemicals that count as "sugars." The ingredients list includes sugar, invert sugar syrup, barley malt extract, and molassses, all of which will contain sugars that likely contribute to the total.

And yet that still doesn't seem to be enough. I was confused at first too, as whole wheat flour only contains roughly a gram of sugars. I consulted a half dozen different products and different nutritional databases, and whole wheat flour and whole wheat berries contain around a gram of sugar per 100 grams. (It varies a bit by wheat variety, but seems to usually be in the range of 0.5-1.5 grams of sugar per 100 grams.)

So what's going on? That only seemingly accounts for maybe 5-6 grams of sugar, as OP notes. I agree that at first it was a mystery to me too. Then I went to the Shreddies website and noticed the description -- "delicious malty, milk-loving squares."

Lacking another explanation, the issue must be in the "malting." At first, one might assume the malt extract is what creates the malty flavor, but whole grains can easily be malted (that is, allowing them to sprout a bit, which also develops natural enzymes in the grain to convert carbohydrates and starches into sugars). The added barley malt, assuming it contains active enzymes, can also assist in this conversion to sugar.

As noted on this Canadian site:

Many varieties of Shreddies either use a malted cereal process or use additions of malt extract. We could not find if Canadian manufactured Shreddies uses Malting. If malting is used the grains would develop enzymes through the germination process that turn the starches into starches and sugars such as maltose through the forced germination process of malting. The resulting rootlets would then be removed and recycled into valuable animal feed.

The malting process provides colour and flavour to the product. There is also a possibility that malting extract may also be used in the flavouring of products. The malt extract is the filtered and evaporated sweet liquid that is extracted and evaporated during the germination process which contains mostly maltose (malt sugar) from the malting process of barley or wheat.

Malting preserves the natural characteristics of whole grain and extracts are nutritious and functional to processing. (Vitamin B, and used as a substitute for refined sugar, and amino acids.)

To my mind, that's the only reasonable explanation, unless Shreddies is made from some bizarre engineered wheat variety that has oodles more sugar than usual. As that site quoted above notes: "Processing information is very difficult to discover on Shreddies." While some products will definitely advertise malting of ingredients as part of their process, I don't know what the labeling requirements in the UK are for this.

However, it's easily possible that malting of the whole-grain wheat could double the sugar content of the final cereal, as is likely the case here. Note that in this case the sugar is not "added," but instead effectively converted from the natural carbohydrates and starches in the whole wheat to sugars. (Also, it's important to note that this process will happen in your digestive system anyway when you eat whole grains, as the human body breaks down many carbohydrates into simpler sugars. I'm not saying there is no nutritional difference, only that the total number of carbohydrates you are ingesting from the whole wheat is likely about the same.)

EDIT -- IMPORTANT NOTE: After further research, I realized I'm wrong about the implications of EU labeling. The relevant information can be found at this link, but there are also UK resources that confirm this interpretation.

As discussed there, Chris H's interpretation may in fact be what's going on here too. That is, they may begin with 96 grams of whole wheat, add 13 grams of sugars (in various forms), then bake the cereal, causing water to evaporate from the wheat, and then still claim that whole wheat is 96% of the total ingredients, even with 13 grams added sugar. It sounds preposterous, but the example near the bottom of the EU regulations linked above says this is actually the way to label this process. The only time when they need to explain this absurdity is if the ingredients required to be labeled with percentages (otherwise known as a quantitative ingredient declaration, or QUID) seem to add up to more than 100%, in which case there needs to be clarification. However, since the packaging doesn't make any statements about the added sugars in the advertising, they aren't required to state the percentage of added sugars. So, if I'm reading these regulations correctly, even though added sugars might constitute 13% of the final product, they can still claim the product has 96% whole wheat. (See the example at point 27 in the EU link above,[SEE ADDITIONAL EDIT BELOW] which shows that the calculation for a QUID is generally the weight of the original ingredient divided by the final weight of the product, regardless of whether weight loss in the ingredient may have significantly changed the percentage in the final product.)

In sum, the sugar content here could be due to malting, or it could be due to a lot of added sugar that is effectively hidden in the ingredients declaration, due to loss of moisture and the bizarre EU method of percentage calculation. Or it could be partly both. I don't know that there's any way to know for certain without chemical analysis of the cereal or further processing details from the manufacturer.

FURTHER EDIT -- To address some concerns that have come up in comments on this answer and Chris H's answer, please note the link to a UK document on QUID that was provided by the commenter. (I found that link before too, but quoted the EU link as more recent. The comment claims the EU link is broken in my answer, but it still works fine for me. Nevertheless, I'm adding this for the sake of completeness and to show a UK source.) In any case, please consult page 14 in the UK link under section 43 to see the same calculation on butter cookies I mentioned above in my last edit. For the sake of completeness, I quote that regulation in detail here:

43. QUID declarations on products (such as cakes, biscuits, pies and cured meats) the composition of which has been changed by cooking or other treatments involving loss of moisture should be based on the amount of the ingoing ingredient expressed as a percentage of the weight of the final product. For example, the butter content of a “butter cookie” would be calculated as follows: Ingredients: List item Weight Flour 100g Sugar 35g Butter 50g Eggs 10g Total mixing bowl 195g Total after baking 169g Formula: 50/169 x 100 = 29.6% Where this calculation would lead to declarations exceeding 100%, the declarations should be replaced with statements giving the amount of the ingredients used to make 100g/ml of the final product (eg “made with Xg/ml of Y per 100g/ml”).

In that case, the butter percentage in the butter cookies is likely overrepresented as a constituent of the final product, since the highest percentage free moisture component in the cookies was the eggs (typically ~75% water compared to ~15% water in butter and even less in flour). Nevertheless, this is the way the EU requires calculations to be done. I don't know whether this calculation method and way of adding sugar was used in OP's case or not, but the regulations appear to allow it.

I often come across bread labeled "100 percent whole wheat." I've always taken this to mean that the grain is 100 percent whole wheat, rather than that whole wheat constitutes 100 percent of the ingredients. Obviously there are other ingredients in bread, like salt, yeast, and water.

I suspect that a similar thing is going on with this cereal. As you point out, the math doesn't work out for the cereal to be 96 percent whole grain wheat (which has relatively little sugar) and 13 percent sugar.

This all tells me that when they write "96 percent whole grain wheat" what they're really saying is that 96 percent of the grain is whole grain.

My lingering question is what the remaining 4 percent is made up of.