Most of the time in Introductory Physics we use the constant acceleration equations, even if it's a Calculus based class. The displacement equation is given as a series of some power of time times a constant, which have various meanings.

\(\displaystyle s = s_0 + v_0t + \dfrac{1}{2}at^2 + \dfrac{1}{6}jt^3 \text{ ...}\)

Here, the s stands for displacement, v for velocity, a for acceleration, and j for "jerk." (Yes folks, this really is the name for it.) I've never heard of a problem that uses any more terms than this one. This is possibly the equation you are referring to when you say you've seen the "cubed" term.

The only other example I've seen is something of the form \(\displaystyle s = f(t)\) , where f(t) is some function of time. (Depending on your textbook some other letter than f might be used.) This is the form we usually reserve for Calculus based problems and you can get velocity, acceleration, etc. by taking derivatives.

-Dan