Number pattern problem 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.
According to the Online Encyclopedia of Integer Sequences, this is the first 6 values of $n$ of the sequence $n^3 - 5n^2 + 7n$
183, because I say so. 

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