Geometry

Question Analysis  
This question involves the relationship between an inscribed sphere and a cube.
The main focus is on determining the cube’s edge length from the sphere’s radius and then calculating the volume difference.  

Key Concept Explanation  
1. Inscribed Sphere in a Cube: The sphere’s diameter equals the cube’s edge length (a = 2r).  
2. Volume of Cube: .  
3. Volume of Sphere: .  

Step-by-Step Solution  
Step 1: Determine the edge length of the cube  
Radius of the sphere () = 9 cm  
Diameter of the sphere =  
Therefore, edge length of the cube () = 18 cm  
Step 2: Calculate the volume of the cube