Sum of cubes of first n even numbers
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)