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

JavaObject Oriented ProgrammingProgramming

## 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