UPDATE: I've added a large $N$ solution for multiples of 3 that slightly betters OP's solution at $3\times (\frac N 3 - 1)^2 + 9$, see end of this post.
Just to show that @humn is not the only one capable of wasting eyewatering amounts of pizza here are
tiny but equal pieces of pizza made using 6 cuts.
$N = 3n$ solution:
to introduce a general solution of limited value,
to include a solution for 7 cuts,
and to acknowledge a better 6-cut solution
What about $n$ cuts?
Hats off to
Paul Panzer’s tasty
which produces more equally sized pieces than
puzzle poser Joe Z.’s general
$n = 6k > 6$ cuts.
The parabolic result-...