Difference between Sum of Cubes and Sum of First N Natural Numbers

Given an integer N, find the absolute difference between sum of the cubes of first N natural numbers and the sum of first N natural numbers.

Input:N = 3Output:30 Sum of first three numbers is 3 + 2 + 1 = 6 Sum of Cube of first three numbers is = 1 + 8 + 27 = 36 Absolute difference = 36 - 6 = 30Input:N = 5Output:210

**Approach:**

- The sum of the cube of first N natural numbers, using the formula:

- The sum of first N numbers, using the formula:

- The absolute difference between both the sums is

where

Below is the implementation of the above approach:

## C++

`// C++ program to find the difference` `// between the sum of the cubes of the` `// first N natural numbers and` `// the sum of the first N natural number` `#include <bits/stdc++.h>` `using` `namespace` `std;` `int` `difference(` `int` `n)` `{` ` ` `int` `S, res;` ` ` `// Sum of first n natural numbers` ` ` `S = (n * (n + 1)) / 2;` ` ` `// Find the required difference` ` ` `res = S * (S - 1);` ` ` `return` `res;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `n = 5;` ` ` `cout << difference(n);` ` ` `return` `0;` `}` |

## Java

`// Java program to find the difference` `// between the sum of the cubes of the` `// first N natural numbers and` `// the sum of the first N natural number` `class` `GFG` `{` `static` `int` `difference(` `int` `n)` `{` ` ` `int` `S, res;` ` ` `// Sum of first n natural numbers` ` ` `S = (n * (n + ` `1` `)) / ` `2` `;` ` ` `// Find the required difference` ` ` `res = S * (S - ` `1` `);` ` ` `return` `res;` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `n = ` `5` `;` ` ` `System.out.print(difference(n));` `}` `}` `// This code is contributed by 29AjayKumar` |

## Python3

`# Python3 program to find the difference ` `# between the sum of the cubes of the ` `# first N natural numbers and ` `# the sum of the first N natural number ` `def` `difference(n) : ` ` ` `# Sum of first n natural numbers ` ` ` `S ` `=` `(n ` `*` `(n ` `+` `1` `)) ` `/` `/` `2` `; ` ` ` `# Find the required difference ` ` ` `res ` `=` `S ` `*` `(S ` `-` `1` `); ` ` ` `return` `res; ` `# Driver Code ` `if` `__name__ ` `=` `=` `"__main__"` `: ` ` ` `n ` `=` `5` `; ` ` ` `print` `(difference(n)); ` ` ` `# This code is contributed by AnkitRai01` |

## C#

`// C# program to find the difference` `// between the sum of the cubes of the` `// first N natural numbers and` `// the sum of the first N natural number` `using` `System;` `class` `GFG` `{` `static` `int` `difference(` `int` `n)` `{` ` ` `int` `S, res;` ` ` `// Sum of first n natural numbers` ` ` `S = (n * (n + 1)) / 2;` ` ` `// Find the required difference` ` ` `res = S * (S - 1);` ` ` `return` `res;` `}` `// Driver Code` `static` `public` `void` `Main ()` `{` ` ` `int` `n = 5;` ` ` `Console.Write(difference(n));` `}` `}` `// This code is contributed by ajit` |

## Javascript

`<script>` `// JavaScript program to find the difference ` `// between the sum of the cubes of the ` `// first N natural numbers and ` `// the sum of the first N natural number ` ` ` ` ` `function` `difference(n) ` ` ` `{ ` ` ` ` ` `let S, res; ` ` ` ` ` `// Sum of first n natural numbers ` ` ` `S = Math.floor((n * (n + 1)) / 2); ` ` ` ` ` `// Find the required difference ` ` ` `res = S * (S - 1); ` ` ` ` ` `return` `res; ` ` ` `} ` ` ` ` ` `// Driver Code ` ` ` `let n = 5; ` ` ` `document.write(difference(n)); ` ` ` `//This code is contributed by Surbhi Tyagi` `</script>` |

**Output:**

210

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