Why do sugar cubes dissolve in water?

Sugar cubes don't actually "dissolve" in water in the sense that a salt might. Sugar breaks apart into individual non-polar sugar molecules. (relative polarity hinges on the specific species of sugar) Sugar makes a homogeneous mixture in water. Adding salt to the equation makes no real difference in the solubility of sugar in water, sugar still refuses to dissociate into ions so it remains sugar, just fragmented at the molecular level.