From a sphere of mass M and radius R , a smaller sphere of radius R...

Volume of removed sphere $$V_{\text{remo }}=\frac{4}{3} \pi\left(\frac{R}{2}\right)^3=\frac{4}{3} \pi R^3\left(\frac{1}{8}\right)$$ Volume of the sphere (remaining) \begin{aligned} &V_{\text{remain }}=\frac{4}{3} \pi R^3-\frac{4}{3} \pi R^3\left(\frac{1}{8}\right) \\ &=\frac{4}{3} \pi R^3\left(\frac{7}{8}\right) \end{aligned} Therefore mass of sphere carved and remaining sphere are at respectively $\frac{1}{8} \mathrm{M}$ and $\frac{7}{8} \mathrm{M}$ Therefore, gravitational force between these two sphere, $$F=\frac{G \mathrm{M} m}{r^2}$$\begin{aligned} &=\frac{G \frac{7 M}{8} \times \frac{1}{8} M}{(3 R)^2}=\frac{7}{64 \times 9} \frac{G M^2}{R^2} \\ &\simeq \frac{41}{3600} \frac{\mathrm{GM}^2}{\mathrm{R}^2} \end{aligned}