Check mate..........

for $1 x 1$ square, there are : $8 x 8$

for $2 x 2$ squares, there are : $7 x 7$

for $3 x 3$ squares, there are : $6 x 6$

...

for $7 x 7$ squares, there are : $2 x 2$

for $8 x 8$ squares, there are (or is in this case) : $1 x 1$

And the sum is : $\boxed{204}$