Don't Count Now !!!

The number of squares on a $n \times n$ chess board is given by $\displaystyle \sum_{k=1}^{n} k^{2}$

No. of $1\times 1$ squares $=64$

No. of $2\times 2$ squares $=49$

No. of $3\times 3$ squares $=36$

No. of $4\times 4$ squares $=25$

No. of $5\times 5$ squares $=16$

No. of $6\times 6$ squares $=9$

No. of $7\times 7$ squares $=4$

No. of $8\times 8$ squares $=1$

So , $Total$ $Squares$ $=\displaystyle \ 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = \boxed{204}$

The formula regarding the particular problem is n(n+1)(2n+1)/6.Therefore by substituting the values,we get the solution

There are 64, (1x1) squares, 49(2x2) squares, 36(3x3) squares, 25(4x4) squares, 16(5x5) squares, 9(6x6) squares, 4(7x7) squares, and, one BIG (8x8) square. So, the total no. of squares = 64+49+36+25+16+9+4+1=204. Hence, the correct answer is 204.