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Sum of square of first n odd numbers

Last Updated : 13 Jun, 2022
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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

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 <iostream>
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 
<?php
// Simple PHP method to find sum 
// of square of first n odd numbers.

function squareSum( $n)
{
    $sum = 0;
    for ($i = 1; $i <= $n; $i++)
        $sum += (2*$i - 1) * (2*$i - 1);
    return $sum;
}


    echo squareSum(8);

// This code is contributed by Vt_m.
?>
JavaScript 
<script>

// Simple Javascript method to find 
// sum of square of first n odd numbers.
function squareSum(n)
{
    let sum = 0;
    for(let i = 1; i <=  n; i++)
        sum += (2 * i - 1) * (2 * i - 1);
        
    return sum;
}

// Driver code
document.write(squareSum(8));

// This code is contributed by souravmahato348

</script>

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 <iostream>
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 
<?php
// Efficient PHP method to find sum of 
// square of first n odd numbers.

function squareSum($n)
{
    return $n * (4 * $n * $n - 1) / 3;
}


    echo squareSum(8);

// This code is contributed by Vt_m.
?>
JavaScript 
<script>

// JavaScript program to find sum of
// square of first n odd numbers.

    function squareSum(n)
    {
        return n*(4*n*n - 1)/3;
    }

// Driver code

            document.write(squareSum(8));

</script>

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.


D

dharmendra_kumar
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