# Sum of square of first n even numbers

• Last Updated : 22 Sep, 2022

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 = 816

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

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## Javascript

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Output:

`816`

Time Complexity: O(n), where n represents the given integer.
Auxiliary Space: O(1), no extra space is required, so it is a constant.

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

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## Javascript

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Output

`816`

Time complexity: O(1) since performing constant operations
Auxiliary Space: O(1) because constant extra space has been used

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