# C++ program to find Sum of cubes of first N Even numbers

Here, we are going to learn how to find the sum of the cubes of first N even numbers in C++ programming language?
Submitted by Vivek Kothari, on November 09, 2018

The problem is we have a number N and we have to find sum of first N Even natural numbers.

Example:

```    Input:
n = 3

Output:
288 (2^3 + 4^3+6^3)
```

A simple solution is given below...

Example 1:

```#include <iostream>
using namespace std;

int calculate(int n)
{
int sum = 0;
for (int i = 1; i <=  n; i++)
sum = sum + (2*i) * (2*i) * (2*i);
return sum;
}

int main()
{
int num = 3;

cout<<"Number is = "<<num<<endl;
cout << "Sum of cubes of first "<<num<<" even number is ="<<calculate(num);

return 0;
}
```

Output

```Number is = 3
Sum of cubes of first 3 even number is =288
```

The efficient approach is discussed below:

```The sum of cubes of first n natural numbers is given by = (n*(n+1) / 2)^2
Sum of cubes of first n natural numbers can be written as...
= 2^3 + 4^3 + .... + (2n)^3
Now take out common term i.e 2^3
= 2^3 * (1^3 + 2^3 + .... + n^3)
= 2^3*  (n*(n+1) / 2)^2
= 8 * ((n^2)(n+1)^2)/4
= 2 * n^2(n+1)^2
```

Now we can apply this formula directly to find the sum of cubes of first n even numbers.

Example 2:

```#include <iostream>
using namespace std;

int calculate(int n)
{
int sum = 2 * n * n * (n + 1) * (n + 1);
return sum;
}

int main()
{
int num = 3;
cout<<"Number is = "<<num<<endl;
cout << "Sum of cubes of first "<<num<<" even number is ="<<calculate(num);
return 0;
}
```

Output

```Number is = 3
Sum of cubes of first 3 even number is =288
```

TOP Interview Coding Problems/Challenges

Comments and Discussions

Ad: Are you a blogger? Join our Blogging forum.
Learn PCB Designing: PCB DESIGNING TUTORIAL

Languages: » C » C++ » C++ STL » Java » Data Structure » C#.Net » Android » Kotlin » SQL
Web Technologies: » PHP » Python » JavaScript » CSS » Ajax » Node.js » Web programming/HTML
Solved programs: » C » C++ » DS » Java » C#
Aptitude que. & ans.: » C » C++ » Java » DBMS
Interview que. & ans.: » C » Embedded C » Java » SEO » HR
CS Subjects: » CS Basics » O.S. » Networks » DBMS » Embedded Systems » Cloud Computing » Machine learning » CS Organizations » Linux » DOS
More: » Articles » Puzzles » News/Updates

© https://www.includehelp.com some rights reserved.