Cells require sugar to grow. This is equally true for healthy cells and cancerous cells. Without sugar we would die. Even if you eat no sugar, your body will produce sugar from whatever you do eat. This is not a matter of opinion but a matter of measured scientific fact.
Eating too much refined sugar does create health problems, but cancer is not one of them. Eating your favorite ice cream once in a while is not going to have any effect on your cancer and it is unlikely to have any other adverse health effects unless you are diabetic or have really bad teeth and it is a huge bowl.