# Sum of squares of the first n even numbers in C Program

CServer Side ProgrammingProgramming

The sum of squares of the first n even numbers means that, we first find the square and add all them to give the sum.

There are two methods to find the sum of squares of the first n even number

## Using Loops

We can use loops to iterate from 1 to n increase number by 1 each time find the square and add it to the sum variable −

### Example

#include <iostream>
using namespace std;
int main() {
int sum = 0, n =12;
for (int i = 1; i <= n; i++)
sum += (2 * i) * (2 * i);
cout <<"Sum of first "<<n<<" natural numbers is "<<sum;
return 0;
}

### Output

Sum of first 12 natural numbers is 2600

The complexity of this program increase by order 0(n). So, for big values of n, code takes time.

## Using Mathematical formula

To deal with this problem a mathematical formula is derived which is Sum of even natural number is 2n(n+1)(2n+1)/3

### Example

#include <iostream>
using namespace std;
int main() {
int n = 12;
int sum = (2*n*(n+1)*(2*n+1))/3;
cout <<"Sum of first "<<n<<" natural numbers is "<<sum;
return 0;
}

### Output

Sum of first 12 natural numbers is 2600