TL, DR: sugar is not a carcinogenic (cancer-causing) substance.
The idea that sugar fuels cancer cells is a fallacy that unfortunately thrives on the Internet. No studies in people have shown that reducing sugar intake prevents or treats cancer. No studies have shown that eating too much sugar causes cancer.
There is no direct link, and therefore no causality, between sugar and cancer.
All cells, including cancer cells, require energy to survive and grow, this energy is glucose. When we eat sugary foods (simple carbohydrates), glucose gets absorbed straight into the bloodstream ready, for cells to use. When we eat starchy food (complex carbohydrates), like pasta, the digestion process breaks them down into glucose. When there are no carbohydrate in our diet, cells can turn fat and protein into glucose as a last resort, because they need glucose to survive. This means that replacing sugar with other energy sources won’t affect the growth of cancer cells.
Remember that a healthy diet includes carbohydrates, for the energy, fibre, minerals and vitamins that they contain. Avoiding healthy, nutritious foods is not a science-based method to prevent any disease. Avoiding sugar will not prevent cancer, as consuming sugar won’t cause cancer. « Cancer » is a group of different diseases triggered by a huge variety of genetic and lifestyle factors.
The only link between cancer and sugar is indirect: excessive sugar intake can lead to weight gain and increase the risk of obesity and diabetes, which may in turn increase the risk of cancer.