The sum of the squares of the first ten natural numbers is,

1² + 2² + … + 10² = 385

The square of the sum of the first ten natural numbers is,

(1 + 2 + … + 10)² = 55² = 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

可以直接依定义计算1² + 2² + … + n²,(1 + 2 + … + n)² 再相减，或者利用简单的初等数学:

\begin{eqnarray} \sum_{i＝1}^na_{i} = \frac{(1+n) n}{2} \end{eqnarray} \begin{eqnarray} \sum_{i＝1}^n a^2_i = \frac{(2n+1)(n+1)n}{6} \end{eqnarray}

25164150

Source:C++