The volume occupied by an atom is greater than the volume of the nucleus by a factor of about

Size of an atom $\approx 10^{-10}$ m; size of a nucleus $\approx 10^{-15}$ m.
Volume is proportional to the cube of the radius.
$\dfrac{\text{Volume of atom}}{\text{Volume of nucleus}} \sim \left(\dfrac{10^{-10}}{10^{-15}}\right)^3 = (10^5)^3 = 10^{15}$
So the atom occupies about $10^{15}$ times the volume of its nucleus; the atom is mostly empty space.