# Sum of square of first n odd numbers

Given a number n, find sum of square of first n odd natural numbers.

Examples :

```Input : 3
Output : 35
12 + 32 + 52 = 35

Input : 8
Output : 680
12 + 32 + 52 + 72 + 92 + 112 + 132 + 152
```

## Recommended: Please solve it on PRACTICE first, before moving on to the solution.

A simple solution is to traverse through n odd numbers and find the sum of square.
Below is the implementation of the approach.

## C++

 `// Simple C++ method to find sum of square of ` `// first n odd numbers. ` `#include ` `using` `namespace` `std; ` ` `  `int` `squareSum(``int` `n) ` `{ ` `    ``int` `sum = 0; ` `    ``for` `(``int` `i = 1; i <=  n; i++) ` `        ``sum += (2*i - 1) * (2*i - 1); ` `    ``return` `sum; ` `} ` ` `  `int` `main() ` `{ ` `    ``cout << squareSum(8); ` `    ``return` `0; ` `} `

## Java

 `// Simple Java method to ` `// find sum of square of ` `// first n odd numbers. ` ` `  `import` `java.io.*; ` ` `  `class` `GFG { ` `     `  `    ``static` `int` `squareSum(``int` `n) ` `    ``{ ` `        ``int` `sum = ``0``; ` `        ``for` `(``int` `i = ``1``; i <=  n; i++) ` `            ``sum += (``2``*i - ``1``) * (``2``*i - ``1``); ` `        ``return` `sum; ` `    ``} ` `      `  `    ``//Driver Code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{    ` `        ``System.out.println(squareSum(``8``)); ` `    ``} ` `} ` ` `  `// This code is contributed by ` `// Nikita tiwari. `

## Python3

 `# Simple Python method  ` `# to find sum of square  ` `# of first n odd numbers. ` `def` `squareSum(n): ` `     `  `    ``sm ``=` `0` `    ``for` `i ``in` `range``(``1``, n ``+` `1``): ` `        ``sm ``+``=` `(``2` `*` `i ``-` `1``) ``*` `(``2` `*` `i ``-` `1``) ` `         `  `    ``return` `sm ` ` `  `# Driver Code ` `n``=``8` `print``(squareSum(n)) ` ` `  `# This code is contributed by Ansu Kumari `

## C#

 `// Simple C# method to find ` `// sum of square of first ` `// n odd numbers. ` `using` `System; ` ` `  `class` `GFG { ` `     `  `    ``static` `int` `squareSum(``int` `n) ` `    ``{ ` `        ``int` `sum = 0; ` `        ``for` `(``int` `i = 1; i <= n; i++) ` `            ``sum += (2*i - 1) * (2*i - 1); ` `        ``return` `sum; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `Main() ` `    ``{  ` `        ``Console.Write(squareSum(8)); ` `    ``} ` `} ` ` `  `// This code is contributed by ` `// vt_m. `

## PHP

 ` `

Output :

```680
```

An efficient solution is to apply below formula.

```sum = n * (4n2 - 1) / 3

How does it work?
Please refer sum of squares of even and odd
numbers for proof.
```

## C++

 `// Efficient C++ method to find sum of  ` `// square of first n odd numbers. ` `#include ` `using` `namespace` `std; ` ` `  `int` `squareSum(``int` `n) ` `{ ` `    ``return` `n*(4*n*n - 1)/3; ` `} ` ` `  `int` `main() ` `{ ` `    ``cout << squareSum(8); ` `    ``return` `0; ` `} `

## Java

 `// Efficient Java method ` `// to find sum of  ` `// square of first n odd numbers. ` ` `  `import` `java.io.*; ` ` `  `class` `GFG { ` `     `  `    ``static` `int` `squareSum(``int` `n) ` `    ``{ ` `        ``return` `n*(``4``*n*n - ``1``)/``3``; ` `    ``} ` `      `  `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``System.out.println(squareSum(``8``)); ` `    ``} ` `} ` ` `  `// This code is contributed by ` `// Nikita tiwari. `

## Python3

 `# Python3 code to find sum ` `# of square of first n odd numbers ` ` `  `def` `squareSum( n ): ` `     `  `    ``return` `int``(n ``*` `( ``4` `*` `n ``*` `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 odd numbers. ` `using` `System; ` ` `  `class` `GFG { ` `     `  `    ``static` `int` `squareSum(``int` `n) ` `    ``{ ` `        ``return` `n * (4 * n * n - 1)/3; ` `    ``} ` `     `  `    ``// driver code     ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``Console.Write(squareSum(8)); ` `    ``} ` `} ` ` `  `// This code is contributed by ` `// Vt_m. `

## PHP

 ` `

Output :

```680
```

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