method of differences?

Question

I have to find a general rule that will work for the pattern below:

(4^3) - (2^2)=60
(5^3) - (3^2)=116
(6^3) - (4^2)=200
(7^3) - (5^2)=318
(8^3) - (6^2)=476

i have figured out this bit...

60 116 200 318 476
....56 84 118 158
........28 34 40
..............6 6

but i can't figure out the rule..
please help

Answer 1

For the series (x+1)^3-(x-1)^2, the difference between adjacent values in the series is, substituting x+1 for x:
(x+1+1)^3 - (x-1+1)^2 - (x+1+1)^3 + (x-1+1)^2, which when you expand and collect together like terms becomes:

3x^2 + 7x + 8

Answer 2

Take f(n) = (n^2 + 4)(n - 1) for n >= 2 to generate your sequence.