The number of atoms in a cubic based unit cell having one atom on each corner and two atoms on each body diagonal is

Number of atoms in each corner of a cube is 8 and the contribution of one atom present at the corner is 1/8. Therefore, the number of atoms at a corner in per unit cell. $8\times \frac{1}{8}=1$ 

Number of atoms on one diagonal is 2. The atoms that are present in diagonal are situated under a cube, therefore their contribution is 1.

There are four diagonals in a cube, therefore number of atoms in diagonals in one unit cell is:

$4\times 2=8$

Total no. of atoms is 9 (1+8)