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

• Difficulty Level : Easy
• Last Updated : 11 Jul, 2022

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```

Recommended Practice

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 ``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' .`

## 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'.`

## 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``))`

## C#

 `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.WriteLine(Square_Diff(n));   ``  ``}``}` `// This code is contributed by akshitsaxena09.`

## PHP

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## Javascript

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Output :

`2640`

Time Complexity: O(1)
Auxiliary Space: O(1)

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