# Sum of fourth power of first n even natural numbers

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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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

 ` `

Output:

``` 15664
```

Time Complexity : O(n)

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

 ` `

Output:

```5664
```

Time Complexity : O(1)

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