Break volume

Hi,

I have to solve the following task.

There is a 3D volume, sampled in space, each point has (x,y,z). This volume has to be cut in order to get smaller sub-volumes. The sizes/shapes of these small sub-volumes are known. The cut operation can be done only in (xy), (yz) and (zx) planes. Of course, this has to be done in a optimal way, to get as many sub-volumes as possible from a single big 3D volume.
I need some starting point for solving this problem. It doesn't matter if it is not offering exactly what I want but at least to give me an idea.

I will appreciate any advice.

thanks,
Paulie