Hello everyone. I am really struggling to wrap my head around proofs by induction. I have a problem that I need help understanding.

1. Prove: 4 + 8 + 12 +...+ 4n = 2n^{2 }+ 2n for all integers n >= 1

Does the base case always have to equal 1? Or is the base case 4. After doing some algebra I ended up with 4.

After the I get the base case I'm having trouble understanding how to come up with the inductive hypothesis and how to put it all in a proof.