# 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 2^{2}+ 4^{2}+ 6^{2}= 56 Input : 8 Output : 816 2^{2}+ 4^{2}+ 6^{2}+ 8^{2}+ 10^{2}+ 12^{2}+ 14^{2}+ 16^{2}

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 <iostream>` `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

`<?php` `// Simple PHP method to find sum of` `// square of first n even numbers.` `function` `squareSum(` `$n` `)` `{` ` ` `$sum` `= 0;` ` ` `for` `(` `$i` `= 1; ` `$i` `<= ` `$n` `; ` `$i` `++)` ` ` `$sum` `+= (2 * ` `$i` `) * (2 * ` `$i` `);` ` ` `return` `$sum` `;` `}` ` ` `echo` `squareSum(8);` `// This code is contributed by vt_m.` `?>` |

## Javascript

`<script>` `// Simple Javascript method to find sum` `// of square of first n even numbers.` `function` `squareSum(n)` `{` ` ` `sum = 0;` ` ` `for` `(let i = 1; i <= n; i++)` ` ` `sum += (2 * i) * (2 * i);` ` ` ` ` `return` `sum;` `}` `// Driver Code` `document.write(squareSum(8));` `// This code is contributed by souravmahato348` `</script>` |

**Output: **

816

An **efficient solution** is to apply below formula.

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 = 2sum = 2 * n * (n + 1) * (2 * n + 1)/3^{2}+ 4^{2}+ .... + (2n)^{2}= 4 * (1^{2}+ 2^{2}+ .... + n^{2}) = 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 <iostream>` `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

`<?php` `// Efficient PHP method to find sum of` `// square of first n even numbers.` `function` `squareSum( ` `$n` `)` `{` ` ` `return` `2 * ` `$n` `* (` `$n` `+ 1) *` ` ` `(2 * ` `$n` `+ 1) / 3;` `}` `echo` `squareSum(8);` `// This code is contributed by vt_m.` `?>` |

## Javascript

`<script>` `// JavaScript program to find sum of` `// square of first n even numbers.` ` ` `function` `squareSum(n)` ` ` `{` ` ` `let sum = 0;` ` ` `for` `(let i = 1; i <= n; i++)` ` ` `sum += (2 * i) * (2 * i);` ` ` `return` `sum;` ` ` `}` `// Driver code` ` ` `document.write(squareSum(8));` `</script>` |

**Output **:

816

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