Mathematically, how many total cubes are in there? (Of any size)

Lets see. 3240 if you divide each small cube into 8 smaller cubes.

That depends. Every possible combination of sizes or just the sum of same-sized cubes for every size? [e.g. (filled with only 1x1x1) + (filled with only 2x2x2) + ... (filled with one 9x9x9)]
Anyway it's gonna be a HUGE number :O

I'm using the standard measurement on the graph paper which is 1/4th of an inch. But yes, that cube could be divided so many different ways.

That number would indeed be huge. You dont have to calculate it if you're not feeling like it. Who would? o.o

Maybe my maths teacher ^^

Right now, there are 405 cubes each measuring 1/2 an inch. Divide those 1/2 inch cubes into 8 smaller cubes, there would be 3240 cubes measuring 1/4 of an inch. Divide those 1/4 inch cubes up into 8 smaller cubes, there would be 25,920 cubes measuring 1/8 of an inch. If you want to get really crazy, divide those 1/8 of an inch cubes into 8 smaller cubes, there would be 207,360 cubes measuring 1/16 of an inch. Please don't make me draw that though... my brain would turn into lava and melt through my body.

I was more referring to how many measures in terms of squares on the paper. It's 9X9X9 with each cube being 1x1x1, then how many 2x2x2, 3x3x3, and so on

It's actually 9x9x5, so it's not an official cube. Dividing it up into 2x2x2 and 3x3x3 is a little tricky because not all sides are multiples of those dimensions. For example, 2x2x2 cubes would only fit into a 8x8x4 cube 32 times with 149 1x1x1 cubes left over to make up the 9x9x5 cube. (2^3)(32)=256+149=405 1x1x1 cubes that we started out with to make up the 9x9x5. If i have to divide that by 2, you get 4.5x4.5x2.5, which means there would be 50.625 2x2x2 cubes. But keep in mind, some of those are not cubes.

For 3x3x3...
3x3x1... 9 3x3x3 cubes with 162 1x1x1 cubes left over or 3x3x1.66... 14.940 3x3x3 cubes.

For 4x4x4...
2x2x1... 4 4x4x4 cubes with 213 1x1x1 cubes left over or 2.25x2.25x1.25... 6.32 cubes.

For 5x5x5...
1x1x1... 1 5x5x5 cube with 280 1x1x1 cubes left over or 1.8x1.8x1... 3.24 cubes.

For 6x6x6...
1x1x5/6... not possible, but 1.5x1.5x.833... 1.8742 cubes.

For 7x7x7...
1x1x5/7... not possible, but 1.22x1.22x.714... 1.06 cubes.

For 8x8x8...
1x1x5/8... not possible, but 1.111x1.111x.625... .77006 cubes.

For 9x9x9...
1x1x9/5... not possible, but 1x1x.555... .5555 cubes.

It get fairly complex, but I hope this explains it.

Oh! I didnt see how deep it went, I just assumed it was a cube too. My bad

Not a problem. I enjoy doing this sort of thing anyway.