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 Practice

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

 ``

Javascript

 ``

Output :

`680`

Time Complexity: O(n), where n represents the given integer.
Auxiliary Space: O(1), no extra space is required, so it is a constant.
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

 ``

Javascript

 ``

Output :

`680`

Time Complexity: O(1), the code will run in a constant time.
Auxiliary Space: O(1), no extra space is required, so it is a constant.

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