# 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 = 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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++ 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 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 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# 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 `

Output:
```210
```

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