Let A and B be two spheres with radii [tex]r_A[tex] and [tex]r_B[/tex], respectively. The ratio between their volumes is
[tex]\dfrac{\frac{4}{3}\pi r_A^3}{\frac{4}{3}\pi r_B^3}=\dfrac{r_A^3}{r_B^3}=\left(\dfrac{r_A}{r_B}\right)^3[/tex]
So, the ratio of the volumes of two spheres is the cube of the ratio between the radii.
Since the two radii are in ratio 1:4, the two volumes will be in ratio 1:64, since 4^3=64.
So, the volume of the Earth is about 64 times the volume of the Moon.
