Chessboard?

A regular chessboard has $32$ black squares and $32$ white squares $\implies 8 \cdot 8 = 64 \ \text{squares}$

However the total number of all squares can be thought of as: $8^2 + 7^2 + 6^2 + \cdots +3^2 + 2^2 + \ \text{and the one large square (whole board)}$ .

Which gives a total of $\boxed{204 \ \text{squares}}$