$$
\begin{array}{l}
\text { 1. Let } A=\{x \mid x=2 n, n \in \mathbf{N}\} \\
B=\{x \mid x=3 n, n \in \mathbf{N}\}, \\
C=\left\{x \mid x=n^{2}, n \in \mathbf{N}\right\} .
\end{array}
$$

Then $A \cap B \cap C=$
1. $\left\{x \mid x=36 n^{2}, n \in \mathbf{N}\right\}$.
Notice that the numbers in $A \cap B \cap C$ are all perfect squares and can be divided by both 2 and 3, thus they can also be divided by 4 and 9. Therefore, $A \cap B \cap C=\left\{x \mid x=36 n^{2}, n \in \mathbf{N}\right\}$.