There are 1,296 different rectangles in all, 204 of which are squares,
counting the square board itself as one, and 1,092 rectangles that are
not squares. The general formula is that a board of n² squares
contains ((n² + n)²)/4 rectangles, of which (2n³ + 3n² + n)/6 are
squares and (3n^4 + 2n³ - 3n² - 2n)/12 are rectangles that are not
squares. It is curious and interesting that the total number of
rectangles is always the square of the triangular number whose side is
n.