Chemsitry: cubic Unit cell problem. Help!?

Question

Spinel is a mineral that contains 37.9% aluminum, 17.1% magnesium, and 45.0% oxygen by mass.
Spinel has a density of 3.57 g/cm3, and the edge of the unit cell is 809 pm (1 pm = 10-12 m) in length.

How many of each type of atom are present in the unit cell?

Answer 1

Consider one cubic meter such mineral, it must weigh 3.57g. and contain 1/(809e-10)^3 = 1.889e21 unit cells.
In one cubic meter such mineral, there are:
Al: 37.9%*3.57g = 1.353g = 0.05015 mole = 3.020e22 atoms
Mg: 17.1%*3.57g=0.6105g=0.02512 mole = 1.513e22 atoms
O: 45.0%*3.57g = 1.607g = 0.1004 mole = 6.046 atoms.
Hence in one unit cell:
Al: 3.020e22 atoms/1.889e21 = 16
Mg: 1.513e22 atoms/1.889e21 = 8
O: 6.046 atoms/1.889e21 = 32