How many squares are on a chess board?
There are:
- 8 * 8 = 64 1x1 squares
- 7 * 7 = 49 2x2 squares
- 6 * 6 = 36 3x3 squares
.....
- 1 * 1 = 1 8x8 squares
Total = 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 204 squares

There are:
- 8 * 8 = 64 1x1 squares
- 7 * 7 = 49 2x2 squares
- 6 * 6 = 36 3x3 squares
.....
- 1 * 1 = 1 8x8 squares
Total = 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 204 squares
Did you figure this yourself or looked it up somewhere?

There are:
- 8 * 8 = 64 1x1 squares
- 7 * 7 = 49 2x2 squares
- 6 * 6 = 36 3x3 squares
.....
- 1 * 1 = 1 8x8 squares
Total = 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 204 squares
i dont get it

if you take a1, b1, a2, b2 that's another square...and so on
ok,got it. ty though those are not squares so it has to be a1a2b1b2 for a square
Now how many cubes are there in a 3D chess board?
Seems like its an easy generalization.
8x8x8 + 7x7x7 + 6x6x6 + ... + 1x1x1
Though it's maybe a better question as to how chess would even be played on a 3D board; what we're really envisioning is a 3D cube with a bunch of sub-cubes.
Another interesting question to ask is how many rectangles exist on a chess board? If you like this stuff, then math might be the field for you!
Do you know?