Total Number of Squares

The number of squares with side 8x8 = 1

Let us consider a mxm square at the upper left corner.

Each time we move the square towards right we get a new square.

Each time we move the square downwards we get a new square.

Since there are 8-m options while going towards left as well as down.

No. of mxm squares = (8-m)*(8-m) = (8-m)²

\dpi{200} \sum_{i=0}^{8} (8-m)^{2} = \sum_{i=0}^{8}m^{2} = \frac{8(8+1)(2\cdot 8+1)}{6}

Answer-204

no.of squares = n(n+1)(2n+1)/6
In our case, with n = 8, this formula gives 8 x 9 x 17/6 = 204.