Number pattern problem

Question

I need some help to figure out the following number pattern:

Find the next number in the following sequence: $3, 2, 3, 12, 35, 78$.

I tired to figure out the difference by add/subtract/multiple/division also tried to find the existing known pattern still could not work it out.

Answer 1

According to the Online Encyclopedia of Integer Sequences, this is the first 6 values of $n$ of the sequence $n^3 - 5n^2 + 7n$

Answer 2

183, because I say so.

(This makes it more than 30 characters, so there!)