# Sum of cubes of first n even numbers

Given a number n, find sum of first n even natural numbers.

Examples:

```Input : 2
Output : 72
2^3 + 4^3 = 72

Input : 8
Output :10368
2^3 + 4^3 + 6^3 + 8^3 + 10^3 + 12^3 + 14^3 + 16^3 = 10368
```

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

A simple solution is to traverse through n even numbers and find the sum of cubes.

## C++

 `// Simple C++ method to find sum of cubes of ` `// first n even numbers. ` `#include ` `using` `namespace` `std; ` ` `  `int` `cubeSum(``int` `n) ` `{ ` `    ``int` `sum = 0; ` `    ``for` `(``int` `i = 1; i <=  n; i++) ` `        ``sum += (2*i) * (2*i) * (2*i); ` `    ``return` `sum; ` `} ` ` `  `int` `main() ` `{ ` `    ``cout << cubeSum(8); ` `    ``return` `0; ` `} `

## Java

 `// Java program to perform  ` `// sum of cubes of first  ` `// n even natural numbers ` ` `  `public` `class` `GFG  ` `{ ` `    ``public` `static` `int` `cubesum(``int` `n) ` `    ``{ ` `        ``int` `sum = ``0``; ` `        ``for``(``int` `i = ``1``; i <= n; i++) ` `            ``sum += (``2` `* i) * (``2` `* i)  ` `                   ``* (``2` `* i); ` `                 `  `        ``return` `sum; ` `    ``} ` `     `  ` `  `    ``// Driver function ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `a = ``8``; ` `        ``System.out.println(cubesum(a)); ` `         `  `    ``} ` `} ` ` `  `// This code is contributed by Akansh Gupta `

## Python3

 `# Python3 program to find sum of  ` `# cubes of first n even numbers ` ` `  `# Function to find sum of cubes ` `# of first n even numbers  ` `def` `cubeSum(n): ` ` `  `    ``sum` `=` `0` `    ``for` `i ``in` `range``(``1``, n ``+` `1``): ` `        ``sum` `+``=` `(``2` `*` `i) ``*` `(``2` `*` `i) ``*` `(``2` `*` `i) ` `    ``return` `sum` ` `  `# Driven code  ` `print``(cubeSum(``8``)) ` ` `  `# This code is contributed by Shariq Raza `

## C#

 `// C# program to perform  ` `// sum of cubes of first  ` `// n even natural numbers ` `using` `System; ` ` `  `public` `class` `GFG  ` `{ ` `    ``public` `static` `int` `cubesum(``int` `n) ` `    ``{ ` `        ``int` `sum = 0; ` `        ``for``(``int` `i = 1; i <= n; i++) ` `            ``sum += (2 * i) * (2 * i)  ` `                ``* (2 * i); ` `                 `  `        ``return` `sum; ` `    ``} ` `     `  ` `  `    ``// Driver function ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `a = 8; ` `        ``Console.WriteLine(cubesum(a)); ` `         `  `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

## PHP

 ` `

Output:

```10368
```

An efficient solution is to apply below formula.

```sum = 2 *  n2(n+1)2

How does it work?

We know that sum of cubes of first
n natural numbers is = n2(n+1)2 / 4

Sum of cubes of first n natural numbers =
2^3 + 4^3 + .... + (2n)^3
= 8 * (1^3 + 2^3 + .... + n^3)
= 8 *  n2(n+1)2 / 4
= 2 *  n2(n+1)2
```

## C++

 `// Efficient C++ method to find sum of cubes of ` `// first n even numbers. ` `#include ` `using` `namespace` `std; ` ` `  `int` `cubeSum(``int` `n) ` `{ ` `    ``return` `2 * n * n * (n + 1) * (n + 1); ` `} ` ` `  `int` `main() ` `{ ` `    ``cout << cubeSum(8); ` `    ``return` `0; ` `} `

## Java

 `// Java program to perform ` `// sum of cubes of first  ` `// n even natural numbers ` ` `  `public` `class` `GFG ` `{ ` `    ``public` `static` `int` `cubesum(``int` `n) ` `    ``{ ` `                 `  `        ``return` `2` `* n * n * (n + ``1``) * (n + ``1``); ` `    ``} ` `     `  ` `  `    ``// Driver function ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `a = ``8``; ` `        ``System.out.println(cubesum(a)); ` `         `  `    ``} ` `} ` ` `  `// This code is contributed by Akansh Gupta `

## Python3

 `# Python3 program to find sum of ` `# cubes of first n even numbers ` ` `  `# Function to find sum of cubes ` `# of first n even numbers  ` `def` `cubeSum(n): ` `     `  `    ``return` `2` `*` `n ``*` `n ``*` `(n ``+` `1``) ``*` `(n ``+` `1``) ` ` `  `# Driven code  ` `print``(cubeSum(``8``)) ` ` `  `# This code is contributed by Shariq Raza `

## C#

 `// C# program to perform ` `// sum of cubes of first  ` `// n even natural numbers ` `using` `System; ` ` `  `class` `GFG ` `{ ` `    ``public` `static` `int` `cubesum(``int` `n) ` `    ``{ ` `        ``return` `2 * n * n *  ` `               ``(n + 1) * (n + 1); ` `    ``} ` `     `  `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `a = 8; ` `        ``Console.WriteLine(cubesum(a)); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

## PHP

 ` `

Output:

`10368`

Sum of cube of first n odd natural numbers

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