I am studying for my exam and came across this question but I am stuck, can someone tell me if I solved this question correctly? $$\sum_{k=1}^{n}({k^3-(k-1)^3})$$ I know that if I plug in zero, I know that I end up with: $$a_0=0^3-\left(0-1\right)^3=1$$
then: $$=1+\sum _{k=1}^nk^3-\left(k-1\right)^3$$ and then finally I do some quick maths to end up with: $$=1+n^3$$
The series begins from $1$, hence we shouldn't start from $0$.
Via telescoping sum, the answer is $n^3$.