Problem:

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.

25164150

Code:The solution may include methods that will be found here: Library.java .

public interface EulerSolution{

public String run();

}
/*
* Solution to Project Euler problem 6
* By Nayuki Minase
*
* http://nayuki.eigenstate.org/page/project-euler-solutions
* https://github.com/nayuki/Project-Euler-solutions
*/

public final class p006 implements EulerSolution {

public static void main(String[] args) {
System.out.println(new p006().run());
}

private static final int N = 100;

public String run() {
int sum = 0;
int sum2 = 0;
for (int i = 1; i <= N; i++) {
sum += i;
sum2 += i * i;
}
/*
* For the mathematically inclined:
*   sum  = N(N + 1) / 2.
*   sum2 = N(N + 1)(2N + 1) / 6.
*/
return Integer.toString(sum * sum - sum2);
}

}