Question 147
The squares of an $8 \times 8$ board are coloured alternatingly black and white. A rectangle consisting of some of the squares of the board is called *important* if its sides are parallel to the sides of the board and all its corner squares are coloured black. The side lengths can be anything from $1$ to $8$ squares. On each of the $64$ squares of the board, we write the number of important rectangles in which it is contained. The sum of the numbers on black squares is $B$, and the sum of the numbers on white squares is $W$. Determine the difference $B-W$.