Suma de cubos de los primeros n números pares

Dado un número n, encuentre la suma de los primeros n números naturales pares. 
Ejemplos: 
 

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

Una solución simple es atravesar n números pares y encontrar la suma de los cubos. 
 

// 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 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 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# 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
// 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.
?>

<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>

Producción:

10368

Una solución eficiente es aplicar la siguiente fórmula.
 

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 

// 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 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 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# 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
// 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.
?>

<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>

Producción:

10368

Suma del cubo de los primeros n números naturales impares
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