A wooden model of a square pyramid has a base edge of 12 cm and an altitude of 8 cm. A cut is made parallel to the base of the pyramid that separates it into two pieces: a smaller pyramid and a frustum. Each base edge of the smaller pyramid is 6 cm and its altitude is 4 cm. How many cubic centimeters are in the volume of the frustum?
The piece that is removed from the original pyramid to create the frustum is itself a square pyramid that is similar to the original pyramid.  The ratio of corresponding side lengths is 1/2, so the piece that was removed has volume $(1/2)^3 = 1/8$ of the volume of the original pyramid.  Therefore, the remaining frustum has volume $1-(1/8) = {7/8}$ of the original pyramid.

The original pyramid has base area $12^2 = 144$ square cm, so its volume is $144\cdot 8/3 = 48\cdot 8$ cubic centimeters.  Therefore, the frustum has volume \[\frac{7}{8}\cdot (48\cdot 8) = 48\cdot 7 = \boxed{336}\text{ cubic centimeters}.\]