1. For any given natural number $n$, if $n^{6}+3 a$ is a positive integer, then
(A) there are infinitely many such $a$
(B) such $a$ exist, but there are only finitely many
(C) such $a$ do not exist
(D) none of the conclusions (A), (B), (C) are correct
(A)

I. Multiple Choice Questions
1. 【Analysis and Solution】For any natural number $k$, take $a=3 n^{4} k+9 n^{2} k^{2}+9 k^{2}$, then $n^{6}+3 a=\left(n^{2}+3 k\right)^{3}$.