14. (15 points) As shown in the figure, a solid cylinder is fixed on the bottom of a sealed cubic container with an edge length of 20 cm. When the container holds $m$ liters of water, the water surface just touches the top base of the cylinder. If the container is inverted, 8 cm of the cylinder is exposed above the water surface. It is known that the base area of the cylinder is $\frac{1}{8}$ of the base area of the cube. Find the volume of the solid cylinder.
【Solution】The blank height in the first cubic container is:
$$
8 \times\left(1-\frac{1}{8}\right)=8 \times \frac{7}{8}=7 \text { (cm); }
$$

The base area of the cubic container is:
$$
20 \times 20=400 \text { (square cm); }
$$

The base area of the cylinder is:
$$
400 \times \frac{1}{8}=50 \text { (square cm); }
$$

The volume of the cylinder is:
$$
\begin{array}{l}
50 \times(20-7) \\
=50 \times 13 \\
=650 \text { (cubic cm); }
\end{array}
$$

Answer: The volume of the solid cylinder is 650 cubic cm.