A compound formed by elements $A$ and $B$ crystallises in a cubic structure where $A$ atoms are present at the corners of a cube and the $B$ atoms are present at the face centres.The formula of the compound is

A-atoms are present at the corners of a cube. So, the number of A-atoms per unit cell =$8\times \frac{1}{8}=1$
Similarly, B-atoms are present at face centres of a cube.
So, the number of B-atoms per unit cell
$=6\times \frac{1}{2}=3$
Hence, the formula of compound is $A{B}_3$.