Bob has a cheese cube and wants to cut it up into exactly $6$ equal pieces for his guests. These guests are professional cheese connoisseurs who will complain if they get less than anyone else.
Bob doesn't have the tools necessary to make arbitrary and precise cuts. He can be precise enough if he slices from a corner to corner or bisecting along an edge, but not randomly through an edge.
The guests only care about volume, the shape of the pieces doesn't matter.
Here's a cube to help you visualize it.
Is it possible for Bob to please his guests?
Edit: Cleaned up unnecessary restrictions.