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

Given an integer n, find the absolute difference between sum of the squares of first n natural numbers and square of sum of first n natural numbers.

Examples :

Input : n = 3 Output : 22.0 Sum of first three numbers is 3 + 2 + 1 = 6 Square of the sum = 36 Sum of squares of first three is 9 + 4 + 1 = 14 Absolute difference = 36 - 14 = 22 Input : n = 10 Output : 2640.0

**Asked in : biwhiz Company **

**Approach :**

1. Find the sum of square of first n natural numbers.

2. Find the sum of first n numbers and square it.

3. Find the absolute difference between both the sums and print it.

Below is the implementation of above approach :

## C++

`// C++ program to find the difference ` `// between sum of the squares of the ` `// first n natural numbers and square ` `// of sum of first n natural number ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `int` `Square_Diff(` `int` `n){ ` ` ` `int` `l, k, m; ` ` ` ` ` `// Sum of the squares of the ` ` ` `// first n natural numbers is ` ` ` `l = (n * (n + 1) * (2 * n + 1)) / 6; ` ` ` ` ` `// Sum of n naturals numbers ` ` ` `k = (n * (n + 1)) / 2; ` ` ` ` ` `// Square of k ` ` ` `k = k * k; ` ` ` ` ` `// Differences between l and k ` ` ` `m = ` `abs` `(l - k); ` ` ` ` ` `return` `m; ` ` ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ` `int` `n = 10; ` ` ` `cout << Square_Diff(n); ` ` ` `return` `0; ` ` ` `} ` ` ` `// This code is contributed by 'Gitanjali' . ` |

*chevron_right*

*filter_none*

## Java

`// Java program to find the difference ` `// between sum of the squares of the ` `// first n natural numbers and square ` `// of sum of first n natural number ` ` ` `public` `class` `GfG{ ` ` ` `static` `int` `Square_Diff(` `int` `n){ ` ` ` `int` `l, k, m; ` ` ` `// Sum of the squares of the ` ` ` `// first n natural numbers is ` ` ` `l = (n * (n + ` `1` `) * (` `2` `* n + ` `1` `)) / ` `6` `; ` ` ` ` ` `// Sum of n naturals numbers ` ` ` `k = (n * (n + ` `1` `)) / ` `2` `; ` ` ` ` ` `// Square of k ` ` ` `k = k * k; ` ` ` ` ` `// Differences between l and k ` ` ` `m = Math.abs(l - k); ` ` ` ` ` `return` `m; ` ` ` `} ` ` ` `// Driver Code ` `public` `static` `void` `main(String s[]) ` `{ ` ` ` `int` `n = ` `10` `; ` ` ` `System.out.println(Square_Diff(n)); ` ` ` `} ` `} ` `// This code is contributed by 'Gitanjali'. ` |

*chevron_right*

*filter_none*

## Python

`# Python3 program to find the difference ` `# between sum of the squares of the ` `# first n natural numbers and square ` `# of sum of first n natural number ` ` ` `def` `Square_Diff(n): ` ` ` ` ` `# sum of the squares of the ` ` ` `# first n natural numbers is ` ` ` `l ` `=` `(n ` `*` `(n ` `+` `1` `) ` `*` `(` `2` `*` `n ` `+` `1` `)) ` `/` `6` ` ` ` ` `# sum of n naturals numbers ` ` ` `k ` `=` `(n ` `*` `(n ` `+` `1` `)) ` `/` `2` ` ` ` ` `# square of k ` ` ` `k ` `=` `k ` `*` `*` `2` ` ` ` ` `# Differences between l and k ` ` ` `m ` `=` `abs` `(l ` `-` `k) ` ` ` ` ` `return` `m ` ` ` `# Driver code ` `print` `(Square_Diff(` `10` `)) ` |

*chevron_right*

*filter_none*

## C#

`// C# program to find the difference ` `// between sum of the squares of the ` `// first n natural numbers and square ` `// of sum of first n natural number ` `using System; ` ` ` `public class GfG{ ` ` ` `static int Square_Diff(int n){ ` ` ` `int l, k, m; ` ` ` `// Sum of the squares of the ` ` ` `// first n natural numbers is ` ` ` `l = (n * (n + 1) * (2 * n + 1)) / 6; ` ` ` ` ` `// Sum of n naturals numbers ` ` ` `k = (n * (n + 1)) / 2; ` ` ` ` ` `// Square of k ` ` ` `k = k * k; ` ` ` ` ` `// Differences between l and k ` ` ` `m = Math.Abs(l - k); ` ` ` ` ` `return m; ` ` ` `} ` ` ` `// Driver Code ` `public static void Main() ` `{ ` ` ` `int n = 10; ` ` ` `Console.Write(Square_Diff(n)); ` ` ` `} ` `} ` `// This code is contributed by 'vt_m'. ` |

*chevron_right*

*filter_none*

## PHP

`<?php ` `// PHP program to find the difference ` `// between sum of the squares of the ` `// first n natural numbers and square ` `// of sum of first n natural number ` ` ` `function` `Square_Diff(` `$n` `) ` `{ ` ` ` ` ` `$l` `; ` ` ` `$k` `; ` ` ` `$m` `; ` ` ` ` ` `// Sum of the squares of the ` ` ` `// first n natural numbers is ` ` ` `$l` `= (` `$n` `* (` `$n` `+ 1) * ` ` ` `(2 * ` `$n` `+ 1)) / 6; ` ` ` ` ` `// Sum of n naturals numbers ` ` ` `$k` `= (` `$n` `* (` `$n` `+ 1)) / 2; ` ` ` ` ` `// Square of k ` ` ` `$k` `= ` `$k` `* ` `$k` `; ` ` ` ` ` `// Differences between ` ` ` `// l and k ` ` ` `$m` `= ` `abs` `(` `$l` `- ` `$k` `); ` ` ` ` ` `return` `$m` `; ` ` ` `} ` ` ` ` ` `// Driver Code ` ` ` `$n` `= 10; ` ` ` `echo` `Square_Diff(` `$n` `); ` ` ` `// This code is contributed by anuj_67 . ` `?> ` |

*chevron_right*

*filter_none*

Output :

2640

## Recommended Posts:

- Sum of squares of first n natural numbers
- Sum of squares of first n natural numbers
- Average of Squares of Natural Numbers
- Sum of square-sums of first n natural numbers
- Square pyramidal number (Sum of Squares)
- Sum of squares of Fibonacci numbers
- Sum of sum of first n natural numbers
- Natural Numbers
- Sum of first N natural numbers which are divisible by X or Y
- Sum of fifth powers of the first n natural numbers
- Sum of kth powers of first n natural numbers
- Sum of cubes of first n odd natural numbers
- Average of first n even natural numbers
- Sum of all odd natural numbers in range L and R
- Sum of first N natural numbers which are divisible by 2 and 7

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.