1. Let $p, q$ be natural numbers, condition A: $p^{3}-q^{3}$ is even; condition B: $p+q$ is even, then,
(A) A is a sufficient but not necessary condition for B;
(B) A is a necessary but not sufficient condition for B;
(C) A is a necessary and sufficient condition for B;
(D) A is neither a sufficient condition nor a necessary condition for B.
1. (C)

If $p^{3}-q^{3}$ is even $\Leftrightarrow p, q$ have the same parity $\Leftrightarrow p+q$ is even.