The volume of the space not filled by the sphere is the difference between the volume of a cube with edge length 6 inches and the volume of a sphere with radius 3 inches.
Cube
The volume of a cube of edge length s is
... V = s³
When the edge length is 6 in, the volume is
... V = (6 in)³ = 216 in³
Sphere
The volume of a sphere with radius r is
... V = (4/3)π·r³
When the radius is 3 in, the volume is
... V = (4/3)π·(3 in)³ = 36π in³
Space
Then the volume of the space between the cube and the sphere is
... Vcube - Vsphere = 216 in³ - 36π in³ ≈ 102.9 in³ . . . . corresponding to choice C