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 



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

C++

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// 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;
}

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Java

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// 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.

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Python3

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# 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

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C#

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// 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.

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PHP

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<?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.
?>

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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++

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// 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;
}

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Java

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// 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.

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Python3

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# 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 

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C#

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// 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.

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PHP

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<?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.
?>

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Output :

680


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Improved By : vt_m