$$Question\ =\ \frac{\left(Q-R\right)}{3}\ Whats\ the\ remainder?$$
$$Statement\ 1\ =\ R\ =P^3$$
There is not sufficient data for Q here.
Hence, statement 1 is not sufficient.
$$Statement\ 2=\ Q\ =\left(P-2\right)^3$$
There is no sufficient data for R
Hence, Statement 2 is not Sufficient.

Statement 1 and 2 together
$$\frac{\left(R\ -\ Q\right)}{3}$$
$$\frac{\left[P^3-\left(P-2\right)^3\right]}{3}\ =\frac{\left[P^3-\left(P^3-2^3\right)\right]}{3}=\frac{2^3}{3}$$
Both statement together are sufficient.
Hence, correct answer is Option C