Problem 6

Question

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.