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Find the number of squares that can be formed on 8 x 8 chess board?

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The number of squares in a n × n chess board will be n2; n varying from 1 to n.

Now, n2 = 12 + 22 + 32 + ⋯ n2

\(\frac{n(n\,+\,1)(2n\,+\,1)}{6}\) …. (i)

Put n = 8 in eq (i), we get

82\(\frac{8\,\times\, (8\, +\, 1)(2\, ×\, 8 ×\, 1)}{6}\)\(\frac{8 \,×\, 9\, ×\, 17}{6}\) = 204

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