Just like beds, placing a dye next to Cake paints it that color

Pretty simple, although I would prefer if it were to change its overall theme (similar to Glazed Terracotta), for example, dyeing cake Blue would make it a blueberry cake, dyeing with Brown would make it chocolate, etc.

Combining different dyes and ingredients make more complicated cakes.

Classic Minecraft Cake, for reference

Cake + Brown Dye = Chocolate Cake

Cake + Blue Dye + Sweet Berries = Blueberry Cake

Cake + Brown Dye + Sweet Berries = Black Forest Cake

Does it add anything to the game? Not really, it's just a simple, fun idea for decorating.