I think you read it already but for the sake of filling this part with text, and for those of you who may have missed the topic, I will restate my question. How many squares are on a chess board?

204

Three score and four squares.

I concur with 204.

# of 1x1 squares = 8*8 = 64

# of 2x2 squares = 7*7 = 49

# of 3x3 squares = 6*6 = 36

# of 4x4 squares = 5*5 = 25

# of 5x5 squares = 4*4 = 16

# of 6x6 squares = 3*3 = 9

# of 7x7 squares = 2*2 = 4

# of 8x8 squares = 1*1 = 1

For a NxN board then it looks like the number of squares is:

This is difficult to determine if you don't have a sizable amount (I'm not sure how many) of pieces, preferably pawns, to occupy the spaces. If you don't have enough, use a folding board which will literally cut the number in half. 

Infinite.

A square is a rectangle, but a rectangle is not a square.

That is because for large values of ONE, ONE approaches TWO, that is, for small values of TWO.

All of 'em.