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Code Mathematics

Sum of cubes of n even natural numbers

The problem involves calculating the sum of the cubes of the first 'n' even natural numbers. An even natural number is a positive integer that is divisible by 2. The task is to find the sum of the cubes of the first 'n' even natural numbers using a specific formula.

Problem Statement

Given a positive integer 'n', the goal is to calculate and display the sum of the cubes of the first 'n' even natural numbers using a predetermined formula.

Example

Let's take an example to illustrate the problem:

Example

  • Given 'n' = 3 (the first 3 even natural numbers are 2, 4, and 6)
  • We need to find the sum of the cubes of these even numbers.

Idea to Solve

The formula for calculating the sum of the cubes of the first 'n' even natural numbers is: 2 × (n × (n + 1))^2.

Pseudocode

function findSumOfCubes(n):
    if n <= 0:
        return
    sum = 2 * ((n * (n + 1)) * (n * (n + 1)))
    print(sum)

# Example usage
n = 3
findSumOfCubes(n)

Algorithm Explanation

  1. The findSumOfCubes function takes 'n' as input.
  2. It first checks if 'n' is less than or equal to 0. If it is, the function returns.
  3. It then calculates the sum of cubes using the formula provided.
  4. The formula involves squaring the product of 'n' and 'n + 1', then multiplying by 2.
  5. The calculated sum is printed as output.

Code Solution

// C Program
// Sum of cubes of n even natural numbers
#include <stdio.h>

void findSunOfCube(int n)
{
	if (n <= 0)
	{
		return;
	}
	// Calculate sum of cube of n natural number
	// Formula : 2×(n×(n+1))²
	double sum = 2 *((n *(n + 1)) *(n *(n + 1)));
	// Display calculated result
	printf("\n %lf", sum);
}
int main()
{
	int n = 3;
	/*
	    n = 3
	*/
	findSunOfCube(n);
	return 0;
}

Output

 288.000000
// Java program for
// Sum of cubes of n even natural numbers
public class Sum
{
    public void findSunOfCube(int n)
    {
        if (n <= 0)
        {
            return;
        }
        // Calculate sum of cube of n natural number
        // Formula : 2×(n×(n+1))²
        double sum = 2 * ((n * (n + 1)) * (n * (n + 1)));
        // Display calculated result
        System.out.print("\n " + sum );
    }
    public static void main(String[] args)
    {
        Sum task = new Sum();

        int n = 3;
        /*
            n = 3
        */
        task.findSunOfCube(n);
    }
}

Output

 288.0
// Include header file
#include <iostream>

using namespace std;
// C++ program for
// Sum of cubes of n even natural numbers
class Sum
{
	public: void findSunOfCube(int n)
	{
		if (n <= 0)
		{
			return;
		}
		// Calculate sum of cube of n natural number
		// Formula : 2×(n×(n+1))²
		double sum = 2 *((n *(n + 1)) *(n *(n + 1)));
		// Display calculated result
		cout << "\n " << sum;
	}
};
int main()
{
	Sum *task = new Sum();
	int n = 3;
	/*
	    n = 3
	*/
	task->findSunOfCube(n);
	return 0;
}

Output

 288
// Include namespace system
using System;
// Csharp program for
// Sum of cubes of n even natural numbers
public class Sum
{
	public void findSunOfCube(int n)
	{
		if (n <= 0)
		{
			return;
		}
		// Calculate sum of cube of n natural number
		// Formula : 2×(n×(n+1))²
		double sum = 2 * ((n * (n + 1)) * (n * (n + 1)));
		// Display calculated result
		Console.Write("\n " + sum);
	}
	public static void Main(String[] args)
	{
		Sum task = new Sum();
		int n = 3;
		/*
		    n = 3
		*/
		task.findSunOfCube(n);
	}
}

Output

 288
package main
import "fmt"
// Go program for
// Sum of cubes of n even natural numbers
type Sum struct {}
func getSum() * Sum {
	var me *Sum = &Sum {}
	return me
}
func(this Sum) findSunOfCube(n int) {
	if n <= 0 {
		return
	}
	// Calculate sum of cube of n natural number
	// Formula : 2×(n×(n+1))²
	sum := 2 * ((n * (n + 1)) * (n * (n + 1)))
	// Display calculated result
	fmt.Print("\n ", sum)
}
func main() {
	var task * Sum = getSum()
	var n int = 3
	/*
	    n = 3
	*/
	task.findSunOfCube(n)
}

Output

 288
<?php
// Php program for
// Sum of cubes of n even natural numbers
class Sum
{
	public	function findSunOfCube($n)
	{
		if ($n <= 0)
		{
			return;
		}
		// Calculate sum of cube of n natural number
		// Formula : 2×(n×(n+1))²
		$sum = 2 * (($n * ($n + 1)) * ($n * ($n + 1)));
		// Display calculated result
		echo("\n ".$sum);
	}
}

function main()
{
	$task = new Sum();
	$n = 3;
	/*
	    n = 3
	*/
	$task->findSunOfCube($n);
}
main();

Output

 288
// Node JS program for
// Sum of cubes of n even natural numbers
class Sum
{
	findSunOfCube(n)
	{
		if (n <= 0)
		{
			return;
		}
		// Calculate sum of cube of n natural number
		// Formula : 2×(n×(n+1))²
		var sum = 2 * ((n * (n + 1)) * (n * (n + 1)));
		// Display calculated result
		process.stdout.write("\n " + sum);
	}
}

function main()
{
	var task = new Sum();
	var n = 3;
	/*
	    n = 3
	*/
	task.findSunOfCube(n);
}
main();

Output

 288
#  Python 3 program for
#  Sum of cubes of n even natural numbers
class Sum :
	def findSunOfCube(self, n) :
		if (n <= 0) :
			return
		
		#  Calculate sum of cube of n natural number
		#  Formula : 2×(n×(n+1))²
		sum = 2 * ((n * (n + 1)) * (n * (n + 1)))
		#  Display calculated result
		print("\n ", sum, end = "")
	

def main() :
	task = Sum()
	n = 3
	#    n = 3
	task.findSunOfCube(n)

if __name__ == "__main__": main()

Output

  288
#  Ruby program for
#  Sum of cubes of n even natural numbers
class Sum 
	def findSunOfCube(n) 
		if (n <= 0) 
			return
		end

		#  Calculate sum of cube of n natural number
		#  Formula : 2×(n×(n+1))²
		sum = 2 * ((n * (n + 1)) * (n * (n + 1)))
		#  Display calculated result
		print("\n ", sum)
	end

end

def main() 
	task = Sum.new()
	n = 3
	#    n = 3
	task.findSunOfCube(n)
end

main()

Output

 288
// Scala program for
// Sum of cubes of n even natural numbers
class Sum()
{
	def findSunOfCube(n: Int): Unit = {
		if (n <= 0)
		{
			return;
		}
		// Calculate sum of cube of n natural number
		// Formula : 2×(n×(n+1))²
		var sum: Double = 2 * ((n * (n + 1)) * (n * (n + 1)));
		// Display calculated result
		print("\n " + sum);
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var task: Sum = new Sum();
		var n: Int = 3;
		/*
		    n = 3
		*/
		task.findSunOfCube(n);
	}
}

Output

 288.0
// Swift 4 program for
// Sum of cubes of n even natural numbers
class Sum
{
	func findSunOfCube(_ n: Int)
	{
		if (n <= 0)
		{
			return;
		}
		// Calculate sum of cube of n natural number
		// Formula : 2×(n×(n+1))²
		let sum: Int = 2 * ((n * (n + 1)) * (n * (n + 1)));
		// Display calculated result
		print("\n ", sum, terminator: "");
	}
}
func main()
{
	let task: Sum = Sum();
	let n: Int = 3;
	/*
	    n = 3
	*/
	task.findSunOfCube(n);
}
main();

Output

  288
// Kotlin program for
// Sum of cubes of n even natural numbers
class Sum
{
	fun findSunOfCube(n: Int): Unit
	{
		if (n <= 0)
		{
			return;
		}
		// Calculate sum of cube of n natural number
		// Formula : 2×(n×(n+1))²
		val sum = 2 * ((n * (n + 1)) * (n * (n + 1)));
		// Display calculated result
		print("\n " + sum);
	}
}
fun main(args: Array < String > ): Unit
{
	val task: Sum = Sum();
	val n: Int = 3;
	/*
	    n = 3
	*/
	task.findSunOfCube(n);
}

Output

 288

Time Complexity

The time complexity of the code is constant, O(1), since the calculations involved in the formula do not depend on the input size 'n'. Regardless of the value of 'n', the number of operations remains the same.

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