8. A box contains 8 balls of the same size, including three balls numbered 1, three balls numbered 2, and two balls numbered 3. The first ball is randomly drawn from the box and then returned. The second ball is then randomly drawn. Let the product of the numbers on the balls drawn the first and second times be $\xi$, then the mathematical expectation $E \xi=$ $\qquad$ .
$$
\begin{array}{l}
\xi=1,2,3,4,6,9, P(\xi=1)=\left(\frac{3}{8}\right)^{2}=\frac{9}{64}, P(\xi=2)=2 \cdot \frac{3}{8} \cdot \frac{3}{8}=\frac{18}{64}, P(\xi=3)=2 \cdot \frac{3}{8} \cdot \frac{2}{8}=\frac{12}{64}, \\
P(\xi=4)=\left(\frac{3}{8}\right)^{2}=\frac{9}{64}, P(\xi=6)=2 \cdot \frac{3}{8} \cdot \frac{2}{8}=\frac{12}{64}, P(\xi=9)=\left(\frac{2}{8}\right)^{2}=\frac{4}{64},
\end{array}
$$

So $E \xi=\frac{9+36+36+36+72+36}{64}=\frac{225}{64}$.