3. For any given positive integer $n, n^{6}+3 m$ is the cube of some positive integer, where $m$ is a positive integer. Then, such $m$(   ).
(A) is unique
(B) there are only two
(C) there are infinitely many
(D) does not exist

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3.C.
$$
\begin{array}{l}
\text { Let } n^{6}+3 m=\left(n^{2}+3 p\right)^{3} \\
=n^{6}+3\left(3 n^{4} p+9 n^{2} p^{2}+9 p^{3}\right) .
\end{array}
$$

Take \( m=3 n^{4} p+9 n^{2} p^{2}+9 p^{3} \). Since \( p \) is any positive integer, there are infinitely many such positive integers \( m \).