If you want to split a cubic piece of butter into 27 smaller cubes, you can easily do it using just 6 slices (imagine the Rubik Cube). However, after every slice you make you can also rearrange the pieces - stack them in different ways on top of each other, so that the number of cuts possibly gets reduced. What is the minimum number of slices you need in order to accomplish the task?
In order to separate the little cube in the center of the butter piece from the rest, you need 6 slices - that's the number of sides it has. Therefore you can't accomplish the task with less than 6 cuts.