Ok it's probably easier to think of this in terms of planes.
one cut is one plane.
two cuts is two planes.
the maximum cuts with three planes is 8 so there needs to be a third plane such that it intersects all divisions of the planes.
this is possible for three planes, see standard 3D cartesian space.
So then is is possible to get a fourth plane to intersect every division of some system of planes like that?
from my intuition alone I think not, just based on how many orthogonal planes you can have in 3D space so that each plane is orthogonal to each plane.
So then it's the plane that intersects the most subdivisions of the planes and so one six times.
So it's under 64
