One possible answer is 4, -122 and the pattern is given by:
f(x)=-29x³/6+37x²/2+7x/3+8 where x goes from 0 to 5 to create the 6 terms:
8, 24, 48, 51, 4, -122.
(You can also use f(x)=-29x³/6+33x²-295x/6+29 to find the xth term, where x starts at 1.)
But the sequence continues:
-356, -727, -1264, -1996, -2952, ...
This seems an unlikely answer and so we are looking for a series which only has 6 terms.
If I find one I’ll let you know...