The number of squares that can be formed on a chess board is

1 unit squares = 8²
2 unit squares = 7²
3 unit squares = 6²

…………………….

…………………….

8 unit squares = 1²

$\therefore$ Total number of squares that can be formed on a chess board

$=8^2+7^2+\dots +1^2=\frac{8(8+1)(16+1)}{6}=204$.