Simplifying Summation from loop with an if statment

Question

I'm having trouble figuring out how to simplify this code to summations since it has an if statement in it.

sum=0
for (i = 1 to n ){
    for (j = 1 to i^2){
        if (j % i ==0) then
            for (k = 1 to j){
                sum++
            }
        }
    }
}

I know the if statement will execute i times every loop.

1%1 = 0
2%2 = 0
4%2 = 0
3%3 = 0
6%3 = 0
9%3 = 0

and so on.

This is what I have so far (see link below), forgive the i^2 notation, I can't post images yet without rep. Again, the inner summation is i^2 not 2 choose i.

http://www.HostMath.com/Show.aspx?Code=%5Csum%5Climits_%7Bi%3D1%7D%5En%5Csum%5Climits_%7Bj%3D1%7D%5Ei%5E%7B2%7D%20%5Csum%5Climits_%7Bk%3D1%7D%5Ej%0A(1)

I want to simplify the inner summation to j, but it only happens, i times. I feel like this is very simple and I am not seeing the obvious connection.

Answer 1

The answer that I marked as correct was wrong. This was the answer that was given to me. I will do my best to say it properly.

The sum from i = 1 to n, of the sum from j = 1 to i squared for even j is equal approximately to the sum from i = 1 to n of i squared times i squared plus one all over 2.

(or the last part again) is equal to approximately:

the sum from i =1 to n of (i^2 * [(i^2) + 1]) / 2 which is Theta n^5.

THIS is the correct answer