Can a computer make a proof by induction?

Can a computer solve the following problem, i.e. make a proof by induction? And why?

Prove by induction that $$\sum_{k=1}^nk^3=\left(\frac{n(n+1)}{2}\right)^2, \, \, \, \forall n\in\mathbb N .$$

I'm doing a Ph.D. in pure maths. I love coding when I wanna have some fun, but I've never got too far in this field. I say my background because maybe there's someone who wants to explain this in a more abstract language there's a chance that I will understand it.

• Are you looking for any technique that is able to prove that statement, i.e. you are not necessarily looking for a machine learning approach, right?
– nbro
Aug 9, 2020 at 10:48