Difference between sum of the squares of and square of sum first n natural numbers.

Problem Statement

With a given number n, write a program to find the difference between sum of the squares of and square of sum first n natural numbers.

Example

n = 3
Squares of first three numbers
= 3x3 + 2x2 + 1x1
= 9 + 4 + 1
= 14

Squares of sum of first three numbers
= (3 + 2 + 1)x(3 + 2 + 1)
= 6x6
= 36

Difference
= 36 - 14
= 22

Example

Live Demo

Following is the program in Java to find the required difference.

public class JavaTester {
   public static int difference(int n){
      //sum of squares of n natural numbers
      int sumSquareN = (n * (n + 1) * (2 * n + 1)) / 6;
      //sum of n natural numbers
      int sumN = (n * (n + 1)) / 2;
      //square of sum of n natural numbers
      int squareSumN = sumN * sumN;
      //difference
      return Math.abs(sumSquareN - squareSumN);
   }
   public static void main(String args[]){
      int n = 3;
      System.out.println("Number: " + n);
      System.out.println("Difference: " + difference(n));
   }
}

Output

Number : 3
Difference: 22