The mass number of iron nucleus is $56$, the nuclear density is:

Volume, $\mathrm{V}=\frac{4}{3}{\mathrm{\pi r}}^3=\frac{4}{3}\mathrm{\pi }{\left(\left(1.2\times {10}^{-15}\right){\mathrm{A}}^{1/3}\right)}^3$
Mass, $\mathrm{m} =\mathrm{A} (1.67\times {10}^{-27}) \mathrm{kg}$

$\text{ density }=\frac{\text{ mass }}{\text{ volume }}=\frac{(1.67\times {10}^{-27})\mathrm{A}}{\frac{4}{3}\pi \times {1.2}^3\times {10}^{-45}\times \mathrm{A}}=2.29\times {10}^{17}{\mathrm{kgm}}^{-3}$