Wings as a math visualization tool...

[micheus]

Dimitri, assuming my comment is right I will try a shot.

So, by considering a cube composed by 4 units (small cubes) and using Wings3d to check the progression of the total amount I got this:

and it means that:
- the big cube composed of 4 smaller cubes of dimensions can group 64 smaller cubes inside of it;
- if we assume the smaller cube has 2 cubes of dimension, then the big cube can group 27 cubes inside of it;
- if we assume the smaller cube has 3 cubes of dimension, then the big cube can group 8 cubes inside of it;
- if we assume the smaller cube has 4 cubes of dimension, then the big cube can group only 1 cubes inside of it;

The total amount of cube representations possible are 100 (64+27+8+1).

As we can notice, we were talking about 4³+3³+2³+1³

Assuming that n is equivalent to the amount the smaller cube that defines the initial cube we can use the equation (ref.):

If everything I wrote is right, now the answer for your question is easy to find:
Tc=((512(512+1))/2) => 17247043584!!!