Sum of square of first n even numbers

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

Examples :

Input : 3
Output : 56 
22 + 42 + 62 = 56

Input : 8
Output : 816
22 + 42 + 62 + 82 + 102 + 122 + 142 + 162 

A simple solution is to traverse through n even numbers and find the sum of square.

C++

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// Simple C++ method to find sum 
// of square of first n even numbers.
#include <iostream>
using namespace std;
  
int squareSum(int n)
{
    int sum = 0;
    for (int i = 1; i <= n; i++)
        sum += (2 * i) * (2 * i);
    return sum;
}
  
// Driver Code
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 even numbers.
import java.io.*;
  
class GFG 
{
    static int squareSum(int n)
    {
        int sum = 0;
        for (int i = 1; i <= n; i++)
            sum += (2 * i) * (2 * i);
        return sum;
    }
      
    // Driver Code
    public static void main(String args[])
                  throws IOException
    {
        System.out.println(squareSum(8));
    }
}
  
// This code is contributed by Nikita Tiwari 

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Python3

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# Simple Python3 code to 
# find sum of square of
# first n even numbers
  
def squareSum( n ):
    sum = 0
    for i in range (0, n + 1):
        sum += (2 * i) * (2 * i)
          
    return sum
  
# driver code
ans = squareSum(8)
print (ans)
  
# This code is contributed by Saloni Gupta

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C#

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// Simple C# method to find sum of
// square of first n even numbers.
using System;
  
class GFG 
{
    static int squareSum(int n)
    {
        int sum = 0;
        for (int i = 1; i <= n; i++)
            sum += (2 * i) * (2 * i);
          
        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 even numbers.
  
function squareSum($n)
{
    $sum = 0;
    for ($i = 1; $i <= $n; $i++)
        $sum += (2 * $i) * (2 * $i);
    return $sum;
}
  
  
    echo squareSum(8);
  
  
// This code is contributed by vt_m.
?>

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Output:

816

An efficient solution is to apply below formula.

sum = 2 * n * (n + 1) * (2 * n + 1)/3

How does it work? 
We know that sum of square of first 
n natural numbers is = n(n+1)/2

Sum of square of first n even natural numbers = 
        22 + 42 + .... + (2n)2
      = 4 * (12 + 22 + .... + n2)
      = 4 * n(n+1)(2n+1) / 6
      = 2 * n(n+1)(2n+1)/3 

C++

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// Efficient C++ method to find sum 
// of square of first n even numbers.
#include <iostream>
using namespace std;
  
int squareSum(int n)
{
    return 2 * n * (n + 1) * 
            (2 * n + 1) / 3;
}
  
// Driver code
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 even numbers.
import java.io.*;
  
class GFG 
{
    static int squareSum(int n)
    {
        return 2 * n * (n + 1) * 
                (2 * n + 1) / 3;
    }
  
    // Driver Code
    public static void main(String args[])
                    throws IOException
    {
        System.out.println(squareSum(8));
    }
}
  
// This code is contributed by Nikita Tiwari 

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Python3

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# Efficient Python3 code to 
# find sum of square of 
# first n even numbers
  
def squareSum( n ):
      
    return int(2 * n * (n + 1) * (2 * 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 even numbers.
using System;
  
class GFG
{
      
    static int squareSum(int n)
    {
        return 2 * n * (n + 1) * (2 * 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 even numbers.
  
  
function squareSum( $n)
{
    return 2 * $n * ($n + 1) * 
             (2 * $n + 1) / 3;
}
  
echo squareSum(8);
  
// This code is contributed by vt_m.
?>

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Output :

816


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Improved By : vt_m