Medium: How to cut a circular cake using 2 parallel cuts, such that each of the 3 resulting pieces has the same volume.
Medium: How to cut a square cake into n pieces, so that each piece has the same amount of cake and same amount of frosting.
Hard: How to cut a cake that already has a hole in it into 2 equal parts (from PCMI's pizza session, originally from Car Talk Puzzler). The PCMI version of the problem contains a diagram, so I give it to you here. Note that you don't know the sizes of the rectangles nor the relative angle of rotation of the inner rectangle.
Yum, cake! Lots of math fun in sharing things!