How do you figure out the surface area to volume ratio of a cube that has sides that are 3cm long?

Hello!
The simplest method is to compute the surface area of the cube, its volume and then find their ratio. Denote the length of a side as b centimeters.
The volume of a cube with the side length b is b^3 (this is the base for defining volumes of more complex figures).
The surface of a cube consists of 6 congruent squares: we may call them upper, lower, left, right, front and rear. The surface of each of these squares is b^2, thus the surface area of a cube is 6b^2.
So the ratio in question is equal to  (6b^2)/(b^3) = 6/b.
If b = 3 cm, the value of this ratio is  6/(3 cm) = 2 (cm)^(-1), which is the answer (yes, the dimension of this quantity is (cm)^(-1) = 1/(cm) ).