What is the volume of the cube (in cubic $\text{cm}$) whose diagonal measures $4\sqrt{3}\text{cm}$?

Let the side length of the cube be $a\text{cm}$.
The diagonal ($d$) of a cube is given by the formula:

$$d=a\sqrt{3}$$

Given that the diagonal is $4\sqrt{3}\text{cm}$:

$$a\sqrt{3}=4\sqrt{3}⟹a=4\text{cm}$$

The volume ($V$) of a cube is given by $V=a^3$:

$$V=4^3=64{\text{cm}}^3$$