Problem 6

Sum square difference

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

$$1^2+2^2+\ldots +10^2=385$$

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

$$(1+2+\ldots+10)^2 = 55^2 = 3025$$

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.

前十个自然数的平方的和是

$$1^2+2^2+\ldots +10^2=385$$

前十个自然数的和的平方是

$$(1+2+\ldots+10)^2 = 55^2 = 3025$$

因此，前十个自然数的平方和与和平方之差是$3025 − 385 = 2640$。

求前一百个自然数的平方的与和平方之差。

译注：注意此处出题人使用的自然数定义不包含$0$。