"I can make cake." This is 'cake' in an uncountable sense. It's similar to saying 'I can make soup' or 'I can make ice cream'. It's an unspecified amount of a certain kind of "stuff". This sounds like you're going to pour a whole lot of cake mixture into a giant rectangular oven tray and bake it. Perhaps you'll bring this tray along to an event and cut the cake up into small portions. "I can make three cakes" This is 'cake' in the countable sense. Perhaps you'll make one lemon cake, one chocolate cake and one fruitcake. These are three individual objects.

I can makes three cakes. Three means that there is more than one cake, therefore it's plural - cakes.

I can make a cake. I can make some cakes. I can make three cakes. It does not make sense to say I can make cake. You need to have something between "make" and "cake" and depending on what that is the word cake is either in its singular or plural form.

"I can make three cakes." is the correct sentence, because you have provided information to inform that there is more than 1 cake.