【Question 3】
Cut a cube into 27 identical smaller cubes. The sum of the surface areas of these smaller cubes is 432 square centimeters larger than the surface area of the large cube. Then, the volume of the large cube is $\qquad$ cubic centimeters.
【Analysis and Solution】
Let the original edge length of the large cube be $3a$ cm, then the edge length of each small cube is $a$ cm; the surface area of each small cube is $6a^2$ square cm;

The surface area of the large cube is $6 \times (3a)^2 = 54a^2$ square cm;
$$
\begin{array}{l}
6a^2 \times 27 - 54a^2 = 432; \\
a^2 = 4; \\
a = 2;
\end{array}
$$

The edge length of the large cube is $2 \times 3 = 6$ cm;
The volume of the large cube is $6^3 = 216$ cubic cm.