# 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

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 <iostream>` `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

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

## Javascript

`<script>` `// JavaScript program to find sum of cubes of` `// first n even numbers.` ` ` `function` `cubeSum(n)` ` ` `{` ` ` `let sum = 0;` ` ` `for` `(let i = 1; i <= n; i++)` ` ` `sum += (2*i) * (2*i) * (2*i);` ` ` `return` `sum;` ` ` `}` ` ` ` ` `document.write(cubeSum(8)); ` `// This code is contributed by Surbhi Tyagi` `</script>` |

Output:

10368

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

sum = 2 * n^{2(n+1)2 }How does it work? We know that sum of cubes of first n natural numbers is = n^{ }^{2}(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 * n^{2}(n+1)^{2}/ 4 = 2 * n^{2}(n+1)^{2}

## C++

`// Efficient C++ method to find sum of cubes of` `// first n even numbers.` `#include <iostream>` `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

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

## Javascript

`<script>` `// javascript program to perform` `// sum of cubes of first` `// n even natural numbers` `function` `cubesum(n)` `{ ` ` ` `return` `2 * n * n * (n + 1) * (n + 1);` `}` `// Driver function` `var` `a = 8;` `document.write(cubesum(a));` `// This code is contributed by Amit Katiyar` `</script>` |

Output:

10368

Sum of cube of first n odd natural numbers

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