You can split a 6″ cake only 112 times.*+Power%5B2%2C113%5D

Here WolframAlpha helpfully calculates that if you double the Planck length 113 times you’ll get just over 6″. Hence, if you start slicing a 6″ cake in half, around cut 112 you’ll end up with slices just above the Planck length and which cannot be sliced further.

So you won’t actually need infinite icing to cover it, but yeah it’ll be a lot.