so If I listed the first few digits of a sequence, is there a method to break it down and determine the general equation for the nth term of a sequence?

for example:

Given:

1, 9, 37, 100, 225, 325

Does there exist a method to determine the equation is $\displaystyle (\frac{x(x+1)}{2})^2 $

or even break it down as the series of $\displaystyle x^3 $