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

• Last Updated : 28 Mar, 2022

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 = 3
Output: 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 = 30

Input: N = 5
Output: 210```

Approach:

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

2. The sum of first N numbers, using the formula:

3. 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 ``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

 ``

Output:

`210`

Time Complexity: O(1)

Auxiliary Space: O(1)

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