A sphere fits snugly inside a 6-in. cube as shown. what is the volume of the region inside the cube but outside the sphere

Assuming that means the diameter is 6in

so then

vsphere = (4/3) pir^3

r=d/2

d=6

6/2=3=r

vcube-vsphere=space

vcube=side^3=6^3=216

vsphere = (4/3) pi3^3=36pi=113.093755

space=216-113.083755=102.9026644707 cubic inches of empty space