Sugar cubes are porous, so craft glue does not work well to glue them together. Normal glue doesn't work either because it's not edible. Mixing 1 cup powdered sugar and 1 teaspoon of water makes an edible icing adhesive, according to Creativebug, Inc.

Professional bakers often use clear Tylose glue or gum glue to adhere fondant together, and either works with sugar cubes as well. CakeJournal says to add 1 teaspoon of Tylose powder to 1 cup of warm water to make the gum glue. A canister of Tylose powder makes a lot of gum glue. Alternatively, marshmallow fluff is a cheap and easy adhesive that can be applied with a toothpick.