# Sum of square of first n even numbers

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

Examples :

```Input : 3
Output : 56
22 + 42 + 62 = 56

Input : 8
Output : 816
22 + 42 + 62 + 82 + 102 + 122 + 142 + 162
```

## Recommended: Please solve it on PRACTICE first, before moving on to the solution.

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

## C++

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

## Java

 `// Simple Java method to find sum of  ` `// square of first n even numbers. ` `import` `java.io.*; ` ` `  `class` `GFG  ` `{ ` `    ``static` `int` `squareSum(``int` `n) ` `    ``{ ` `        ``int` `sum = ``0``; ` `        ``for` `(``int` `i = ``1``; i <= n; i++) ` `            ``sum += (``2` `* i) * (``2` `* i); ` `        ``return` `sum; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String args[]) ` `                  ``throws` `IOException ` `    ``{ ` `        ``System.out.println(squareSum(``8``)); ` `    ``} ` `} ` ` `  `// This code is contributed by Nikita Tiwari  `

## Python3

 `# Simple Python3 code to  ` `# find sum of square of ` `# first n even numbers ` ` `  `def` `squareSum( n ): ` `    ``sum` `=` `0` `    ``for` `i ``in` `range` `(``0``, n ``+` `1``): ` `        ``sum` `+``=` `(``2` `*` `i) ``*` `(``2` `*` `i) ` `         `  `    ``return` `sum` ` `  `# driver code ` `ans ``=` `squareSum(``8``) ` `print` `(ans) ` ` `  `# This code is contributed by Saloni Gupta `

## C#

 `// Simple C# method to find sum of ` `// square of first n even numbers. ` `using` `System; ` ` `  `class` `GFG  ` `{ ` `    ``static` `int` `squareSum(``int` `n) ` `    ``{ ` `        ``int` `sum = 0; ` `        ``for` `(``int` `i = 1; i <= n; i++) ` `            ``sum += (2 * i) * (2 * i); ` `         `  `        ``return` `sum; ` `    ``} ` `     `  `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``Console.Write(squareSum(8)); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

## PHP

 ` `

Output:

`816`

An efficient solution is to apply below formula.

```sum = 2 * n * (n + 1) * (2 * n + 1)/3

How does it work?
We know that sum of square of first
n natural numbers is = n(n+1)/2

Sum of square of first n even natural numbers =
22 + 42 + .... + (2n)2
= 4 * (12 + 22 + .... + n2)
= 4 * n(n+1)(2n+1) / 6
= 2 * n(n+1)(2n+1)/3

```

## C++

 `// Efficient C++ method to find sum  ` `// of square of first n even numbers. ` `#include ` `using` `namespace` `std; ` ` `  `int` `squareSum(``int` `n) ` `{ ` `    ``return` `2 * n * (n + 1) *  ` `            ``(2 * n + 1) / 3; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``cout << squareSum(8); ` `    ``return` `0; ` `} `

## Java

 `// Efficient Java method to find sum  ` `// of square of first n even numbers. ` `import` `java.io.*; ` ` `  `class` `GFG  ` `{ ` `    ``static` `int` `squareSum(``int` `n) ` `    ``{ ` `        ``return` `2` `* n * (n + ``1``) *  ` `                ``(``2` `* n + ``1``) / ``3``; ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String args[]) ` `                    ``throws` `IOException ` `    ``{ ` `        ``System.out.println(squareSum(``8``)); ` `    ``} ` `} ` ` `  `// This code is contributed by Nikita Tiwari  `

## Python3

 `# Efficient Python3 code to  ` `# find sum of square of  ` `# first n even numbers ` ` `  `def` `squareSum( n ): ` `     `  `    ``return` `int``(``2` `*` `n ``*` `(n ``+` `1``) ``*` `(``2` `*` `n ``+` `1``) ``/` `3``) ` ` `  `# driver code ` `ans ``=` `squareSum(``8``) ` `print` `(ans) ` ` `  `# This code is contributed by Saloni Gupta `

## C#

 `// Efficient C# method to find sum  ` `// of square of first n even numbers. ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `    ``static` `int` `squareSum(``int` `n) ` `    ``{ ` `        ``return` `2 * n * (n + 1) * (2 * n + 1) / 3; ` `    ``} ` `     `  `    ``// driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``Console.Write(squareSum(8)); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

## PHP

 ` `

Output :

`816`

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