jmc

All of the squares of size $5\times 5$, $4\times 4$, and $3\times 3$ contain the black square and there are $$1^2+2^2+3^2=14$$of these. In addition, 4 of the $2\times 2$ squares and 1 of the $1\times 1$ squares contain the black square, for a total of $14+4+1=\boxed{19}$.