The edge length or side of the cube be 'a', and the radius of each particle be 'r'.
a=2r
The volume of cube =a3
(2r)3=8r3
In a simple cube, each unit cell has only one sphere,
The volume of sphere =4 πr3/3
Packing efficiency=Volume if a sphere*100%/Volume of the cube
4/3πr3×100/8r3=52.4%