All edges of a cube are expanding at a rate of 3 centimeters per second.
(a) How fast is the volume changing when each edge is 4 centimeter(s)?
(b) How fast is the volume changing when each edge is 9 centimeters?
Let a denote the edge of the cube. Then
$\displaystyle V = a^3$
That means:
$\displaystyle \dfrac{dV}{dt} = 3a^2 \cdot \dfrac{d a}{dt}$
You already know $\displaystyle a = 4\, cm\, \text{and } \dfrac{d a}{dt} = 3 \frac{cm}s$
I've got $\displaystyle \dfrac{dV}{dt} = 144\,\frac{cm^3}{s}$
b) has to be done in just the same way. I leave this part for you.