How do I construct a proof by induction?

There are typically 4 steps: proving the base case, making an assumption, making the inductive step and finally concluding the proof.

The base case consists of proving that a statement is true for n = 1, the assumption to make is that the statement holds true for n = k, the trickiest part is the inductive step which is proving that the statement is true for n = k + 1 as long as it is true for n = k, and finally the simplest part is wrapping up the proof with a concise statement.

An example of a statement to prove is that n^3 + 2n is always divisible by 3 which I can go through using the whiteboard if needed.