Are there typos in the problem?
What is the cubic eqaution for the follwing coordinates?
. . (1,10), (2,23), (3,38), (4,55), (5,74), (6,96), (7,120), (8,149)
There is no cubic that passes through these points!
In fact, the first five points lie on a parabola: .
. . and the other three points are quite "close" to the parabola.