Given a number n, find the sum of first n even natural numbers.
Examples:
Input : 2 Output : 72 2^3 + 4^3 = 72
Input : 8 Output :10368 2^3 + 4^3 + 6^3 + 8^3 + 10^3 + 12^3 + 14^3 + 16^3 = 10368
A simple solution is to traverse through n even numbers and find the sum of cubes.
C++
// Simple C++ method to find sum of cubes of // first n even numbers. #include <iostream> using namespace std;
int cubeSum( int n)
{ int sum = 0;
for ( int i = 1; i <= n; i++)
sum += (2*i) * (2*i) * (2*i);
return sum;
} int main()
{ cout << cubeSum(8);
return 0;
} |
Java
// Java program to perform // sum of cubes of first // n even natural numbers public class GFG
{ public static int cubesum( int n)
{
int sum = 0 ;
for ( int i = 1 ; i <= n; i++)
sum += ( 2 * i) * ( 2 * i)
* ( 2 * i);
return sum;
}
// Driver function
public static void main(String args[])
{
int a = 8 ;
System.out.println(cubesum(a));
}
} // This code is contributed by Akansh Gupta |
Python3
# Python3 program to find sum of # cubes of first n even numbers # Function to find sum of cubes # of first n even numbers def cubeSum(n):
sum = 0
for i in range ( 1 , n + 1 ):
sum + = ( 2 * i) * ( 2 * i) * ( 2 * i)
return sum
# Driven code print (cubeSum( 8 ))
# This code is contributed by Shariq Raza |
C#
// C# program to perform // sum of cubes of first // n even natural numbers using System;
public class GFG
{ public static int cubesum( int n)
{
int sum = 0;
for ( int i = 1; i <= n; i++)
sum += (2 * i) * (2 * i)
* (2 * i);
return sum;
}
// Driver function
public static void Main()
{
int a = 8;
Console.WriteLine(cubesum(a));
}
} // This code is contributed by vt_m. |
PHP
<?php // Simple PHP method to // find sum of cubes of // first n even numbers. function cubeSum( $n )
{ $sum = 0;
for ( $i = 1; $i <= $n ; $i ++)
$sum += (2 * $i ) *
(2 * $i ) *
(2 * $i );
return $sum ;
} // Driver Code echo cubeSum(8);
// This code is contributed by vt_m. ?> |
Javascript
<script> // JavaScript program to find sum of cubes of // first n even numbers. function cubeSum(n)
{
let sum = 0;
for (let i = 1; i <= n; i++)
sum += (2*i) * (2*i) * (2*i);
return sum;
}
document.write(cubeSum(8));
// This code is contributed by Surbhi Tyagi </script> |
Output:
10368
Time Complexity: O(n)
Auxiliary Space: O(1)
An efficient solution is to apply below formula.
sum = 2 * n2(n+1)2 How does it work? We know that sum of cubes of first n natural numbers is = n2(n+1)2 / 4 Sum of cubes of first n natural numbers = 2^3 + 4^3 + .... + (2n)^3 = 8 * (1^3 + 2^3 + .... + n^3) = 8 * n2(n+1)2 / 4 = 2 * n2(n+1)2
Example
C++
// Efficient C++ method to find sum of cubes of // first n even numbers. #include <iostream> using namespace std;
int cubeSum( int n)
{ return 2 * n * n * (n + 1) * (n + 1);
} int main()
{ cout << cubeSum(8);
return 0;
} |
Java
// Java program to perform // sum of cubes of first // n even natural numbers public class GFG
{ public static int cubesum( int n)
{
return 2 * n * n * (n + 1 ) * (n + 1 );
}
// Driver function
public static void main(String args[])
{
int a = 8 ;
System.out.println(cubesum(a));
}
} // This code is contributed by Akansh Gupta |
Python3
# Python3 program to find sum of # cubes of first n even numbers # Function to find sum of cubes # of first n even numbers def cubeSum(n):
return 2 * n * n * (n + 1 ) * (n + 1 )
# Driven code print (cubeSum( 8 ))
# This code is contributed by Shariq Raza |
C#
// C# program to perform // sum of cubes of first // n even natural numbers using System;
class GFG
{ public static int cubesum( int n)
{
return 2 * n * n *
(n + 1) * (n + 1);
}
// Driver code
public static void Main()
{
int a = 8;
Console.WriteLine(cubesum(a));
}
} // This code is contributed by vt_m. |
PHP
<?php // Efficient PHP code to // find sum of cubes of // first n even numbers. function cubeSum( $n )
{ return 2 * $n * $n *
( $n + 1) * ( $n + 1);
} // Driver code echo cubeSum(8);
// This code is contributed by vt_m. ?> |
Javascript
<script> // javascript program to perform // sum of cubes of first // n even natural numbers function cubesum(n)
{ return 2 * n * n * (n + 1) * (n + 1);
} // Driver function var a = 8;
document.write(cubesum(a)); // This code is contributed by Amit Katiyar </script> |
Output:
10368
Time Complexity: O(1)
Auxiliary Space: O(1)