Thanks for your question - I think this speaks a lot to people who are very worried about “getting cancer” from something in the diet. As with most things, the research can vary place-to-place, food-to-food, etc. 

One thing to keep in mind is that there are a variety of catalysts that lead to increased cancer risk. We know most of them (smoking, genetics, excessive alcohol intake, just to name a few), but it is very hard to discern foods - well, because we do not just eat ONE food our entire life (unlike smoking - studies looking at smokers usually stick with cigarettes). Also - trying to find associations between one food and a specific TYPE of cancer is also difficult - i.e. one food may not have any association with stomach cancer, but have an increased risk of promoting pancreatic cancer. So, looking at research, it is difficult to provide you with one specific answer - but here goes.

According to research, excessive glucose intake (which can be in the form of sugar) may lead to increased risk of certain cancers. There has been research looking at ovarian cancer and pancreatic cancer, for instance. The research puts a BIG “may” out there, because there is simply not enough evidence to suggest a true correlation. However, with most things, moderation is key - so preventing consumption of excessive sugar intake (including sugar-laden beverages, sweets, desserts, refined carbohydrates, etc.) is never a bad things for anyone. Will it prevent cancer? It is hard to say at this time. Websites and other opinion-based sources will say “sugar feeds cancer” and “accelerates cancer growth,” but this has not been confirmed through evidence based research and therefore can not be considered true enough to actually recommend its effectiveness. 

In response to your other question - If a person is gluten sensitive, they have an allergic response (which has to do with histamine - just like seasonal allergies) to gluten. This response, whether it be from pollen, ragweed, or gluten, causes inflammation. As discussed in previous posts, there are plenty of ramifications from recurrent inflammation (including increased cancer risk). With that said, there is some evidence to suggest that excessive gluten intake (from high consumption of carbohydrates that contain gluten) may result in sensitivity and therefore, inflammation. One could deduct from this that gluten intake without sensitivity may lead to inflammation and therefore cancer, but that is quite a leap. 

With both of these questions, there is one take away. AVOID excessive intake of sugars, carbohydrates, sugary-laden beverages, and refined foods. Keep it in moderation by following the recommendations mentioned in The Slice Plan. There is NO LINK between any type and cancer and intake of any food in moderation. Your best bet is to not worry about developing cancer from foods, and simply enjoy a diet rich in whole foods full of variety and flavor. 

I hope this helps. Happy Eating!