# Sum of fourth power of first n even natural numbers

• Last Updated : 12 Sep, 2022

Write a program to find the sum of fourth power of first n even natural numbers.
24 + 44 + 64 + 84 + 104 +………+2n4
Examples:

```Input  :   3
Output :  1568
24 +44 +64 = 1568
Input  :   6
Output :  36400
24 + 44 + 64 + 84 + 104 + 124 ```

Naive Approach :- In this Simple finding the fourth powers of the first n even natural numbers is iterate a loop from 1 to n time. Every i’th iteration store in variable and continue till (i!=n). This is take a O(N) Time Complexity.

## C++

 `// CPP Program to find the sum of fourth powers of``// first n even natural numbers``#include ``using` `namespace` `std;` `// calculate the sum of fourth power of first n even``// natural numbers``long` `long` `int` `evenPowerSum(``int` `n)``{``    ``long` `long` `int` `sum = 0;``    ``for` `(``int` `i = 1; i <= n; i++) {` `        ``// made even number``        ``int` `j = 2 * i;``        ``sum = sum + (j * j * j * j);``    ``}``    ``return` `sum;``}` `// Driven Program``int` `main()``{``    ``int` `n = 5;``    ``cout << evenPowerSum(n) << endl;``    ``return` `0;``}`

## Java

 `// Java Program to find the sum of fourth powers of``// first n even natural numbers` `import` `java.io.*;` `class` `GFG {``    ` `    ``// calculate the sum of fourth power of first``    ``// n even natural numbers``    ``static` `long` `evenPowerSum(``int` `n)``    ``{``        ``long` `sum = ``0``;``        ``for` `(``int` `i = ``1``; i <= n; i++)``        ``{``    ` `            ``// made even number``            ``int` `j = ``2` `* i;``            ``sum = sum + (j * j * j * j);``        ``}``        ` `        ``return` `sum;``    ``}` `    ``// Driven Program``    ``public` `static` `void` `main (String[] args) {``        ` `        ``int` `n = ``5``;``        ``System.out.println(evenPowerSum(n));``    ``}``}` `/*This code is contributed by vt_m.*/`

## Python3

 `# Python3 Program to find``# the sum of fourth powers of``# first n even natural numbers` `# calculate the sum of fourth``# power of first n even``# natural numbers``def` `evenPowerSum(n):``    ``sum` `=` `0``;``    ``for` `i ``in` `range``(``1``, n ``+` `1``):``        ` `        ``# made even number``        ``j ``=` `2` `*` `i;``        ``sum` `=` `sum` `+` `(j ``*` `j ``*` `j ``*` `j);``    ``return` `sum``;` `# Driver Code``n ``=` `5``;``print``(evenPowerSum(n));` `# This is contributed by mits.`

## C#

 `// C# Program to find the sum of fourth powers of``// first n even natural numbers``using` `System;` `class` `GFG {` `    ``// calculate the sum of fourth power of``    ``// first n even natural numbers``    ``static` `long` `evenPowerSum(``int` `n)``    ``{``        ` `        ``long` `sum = 0;``        ``for` `(``int` `i = 1; i <= n; i++) {` `            ``// made even number``            ``int` `j = 2 * i;``            ``sum = sum + (j * j * j * j);``        ``}``        ` `        ``return` `sum;``    ``}` `    ``// Driven Program``    ``public` `static` `void` `Main()``    ``{``        ``int` `n = 5;``        ` `        ``Console.Write(evenPowerSum(n));``    ``}``}` `// This code is contributed by vt_m.`

## PHP

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## Javascript

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Output:

` 15664`

Time Complexity : O(n)

Auxiliary Space: O(1) as it is using constant space for variables

Efficient Approach :- An efficient solution is to use direct mathematical formula which is derived below, This is take only O(1) Time Complexity.

Sum of fourth power of first n even natural number = 8*(n*(n+1)*(2*n+1)(3*n2+3*n -1))/15
How does this formula work?
Sum of fourth power of natural numbers is = (n(n+1)(2n+1)(3n2+3n-1))/30
we need even natural number so we multiply each term 24
= 24(14 + 24 + 34 + ………… +n4
= (24 + 44 + 64 + ………… +2n4
= 24*(sum of fourth power natural number)
= 16*(n*(n+1)*(2*n+1)(3*n2+3*n -1))/30
= 8*(n*(n+1)*(2*n+1)(3*n2+3*n -1))/15

## C++

 `// CPP Program to find the sum of fourth powers of``// first n even natural numbers``#include ``using` `namespace` `std;` `// calculate the sum of fourth power of first n``// even natural numbers``long` `long` `int` `evenPowerSum(``int` `n)``{``    ``return` `(8 * n * (n + 1) * (2 * n + 1) *``          ``(3 * n * n + 3 * n - 1)) / 15;``}` `// Driven Program``int` `main()``{``    ``int` `n = 4;``    ``cout << evenPowerSum(n) << endl;``    ``return` `0;``}`

## Java

 `// JAVA Program to find the sum of fourth powers of``// first n even natural numbers` `import` `java.io.*;` `class` `GFG {``        ` `    ``// calculate the sum of fourth power of first n``    ``// even natural numbers``    ``static` `long` `evenPowerSum(``int` `n)``    ``{``        ``return` `(``8` `* n * (n + ``1``) * (``2` `* n + ``1``) *``                   ``(``3` `* n * n + ``3` `* n - ``1``)) / ``15``;``    ``}``    ` `    ``// Driven Program``    ``public` `static` `void` `main (String[] args) {``        ` `        ``int` `n = ``4``;``        ``System.out.println(evenPowerSum(n));``    ``}``}` `/* This code is contributed by vt_m. */`

## Python3

 `# Python3 Program to find``# the sum of fourth powers``# of first n even natural``# numbers` `# calculate the sum of``# fourth power of first n``# even natural numbers``def` `evenPowerSum(n):``    ``return` `(``8` `*` `n ``*` `(n ``+` `1``) ``*``           ``(``2` `*` `n ``+` `1``) ``*` `(``3` `*``            ``n ``*` `n ``+` `3` `*` `n ``-` `1``)) ``/` `15``;` `# Driver Code``n ``=` `4``;``print` `(``int``(evenPowerSum(n)));` `# This code is contributed by mits`

## C#

 `// C# Program to find the sum of fourth powers of``// first n even natural numbers` `using` `System;` `class` `GFG {` `    ``// calculate the sum of fourth power of first n``    ``// even natural numbers``    ``static` `long` `evenPowerSum(``int` `n)``    ``{``        ``return` `(8 * n * (n + 1) * (2 * n + 1) *``                     ``(3 * n * n + 3 * n - 1)) / 15;``    ``}` `    ``// Driven Program``    ``public` `static` `void` `Main()``    ``{``        ``int` `n = 4;``        ` `        ``Console.Write(evenPowerSum(n));``    ``}``}` `/* This code is contributed by vt_m.*/`

## PHP

 ``

## Javascript

 ``

Output:

`5664`

Time Complexity : O(1)

Auxiliary Space: O(1)

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