The sum of the squares of the first ten natural numbers is, $$1^2 + 2^2 + ... + 10^2 = 385$$ The square of the sum of the first ten natural numbers is, $$(1 + 2 + ... + 10)^2 = 55^2 = 3025$$ 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.