The number of carbon atoms per unit cell of the diamond is

Diamond has an FCC lattice with 4 extra atoms in alternate tetrahedral holes: $8 \times \frac{1}{8} + 6 \times \frac{1}{2} + 4 = 8$ atoms per unit cell. Four atoms per cell is the count for a simple FCC lattice, which ignores the atoms in the tetrahedral holes.