Hi, if there is a rectangular parallelopipe x*y*z ,made of 1*1*1 units then into how many parts can it be sliced by appling cuts at most n times parallel to it's parallel sides?

E.g if x=y=z=2 and n=3

then number of parts = 8.

If x=y=z then i think answer is x^n

but what for other cases?

Note: the cuts are made along integer co-ordinates.

Thanks.