The packing fraction for a body centered cube is 

In body centered cubic structure, each unit cell has two atoms,

$$\begin{gathered} \mathrm{Packing} \mathrm{efficiency}=\frac{\mathrm{Volume} \mathrm{occupied} \mathrm{by} \mathrm{two} \mathrm{sphers} \mathrm{in} \mathrm{unit} \mathrm{cell}}{\mathrm{Total} \mathrm{volume} \mathrm{of} \mathrm{unit} \mathrm{cell}}\times 100 \\ =\frac{2\times \left({\displaystyle \frac{4}{3}}\right){\mathrm{\pi r}}^3\times 100}{{\left({\displaystyle \frac{4}{\sqrt{3}}}\right)}^3}=68\% (\mathrm{Since}, \mathrm{a}=\frac{4}{\sqrt{3}}\mathrm{r}) \end{gathered}$$