8. The set of points $\left\{(x, y) \left\lvert\, \lg \left(x^{3}+\frac{1}{3} y^{3}+\frac{1}{9}\right)=\lg x+\lg y\right.\right\}$ represented by enumeration is


$$
\begin{array}{l}
\text { 8. }\left\{\left(\frac{\sqrt[3]{3}}{3}, \frac{\sqrt[3]{9}}{3}\right)\right\} \text {. } \\
x^{3}+\frac{1}{3} y^{3}+\frac{1}{9}=x y(x>0, y>0) \text {, and } x^{3}+\frac{1}{3} y^{3}+\frac{1}{9} \geqslant 3 \cdot \sqrt[3]{x^{3} \cdot \frac{1}{3} y^{3} \cdot \frac{1}{9}}=x y \text {, } \\
\end{array}
$$

The equality holds if and only if $x^{3}=\frac{1}{3} y^{3}=\frac{1}{9}$, i.e., $x=\frac{\sqrt[3]{3}}{3}, y=\frac{\sqrt[3]{9}}{3}$.