The squares of an $8 \times 8$ board are colored alternately 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 colored 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 the black squares is $B$, and the sum of the numbers on the white squares is $W$. Determine the difference $B - W$.

Let's think step by step and output the final answer within \boxed{}.
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