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)
This article is contributed by Dharmendra kumar. If you like neveropen and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the neveropen main page and help other Geeks.
Please write comments if you find anything incorrect, or if you want to share more information about the topic discussed above.
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
