I am currently studying programming and one of the problems I had wanted me to get the initial value $n$ of the following summation which I know the result $m$ (the problem isn't exactly this, but I turned the problem into this):
$$\sum_{x=0}^{n-1}(n-x)^{3}=m$$
I am posting these here instead of a programming site because I don't want the answer in code, but just the math behind it. I would do it myself, but I'm still coursing high school and I haven't seen something like this before, so if someone could please explain me how would I do this, or maybe just tell me what should I look for to learn how to do these things, it would be greatly appreciated.
Also, as I don't know exactly what branch of math this is, I don't know which tag to use, so if I got the wrong one, please let me know.
We have $$m=\sum_{x=0}^{n-1}(n-x)^{3}=\sum_{k=1}^n k^3=\frac{n^2(n+1)^2}4$$ by a well-known formula that is easily proved by induction, if you've leaned about that.
Can you take it from here?