The ratio of the volume of a cube to that of the sphere which exactly fits inside the cube is

$6 : \pi $

We know that,

Diameter of the sphere = Edge of the cube

So, the diameter of the sphere = 2r = a ( edge of the cube)

So, there volume will be in the ratio of ,

Volume of cube : Volume of sphere

a³ : 4/3πr³

(2r)³ : 4/3πr³

8r³ : 4/3πr³

$6 : \pi $