Solution

Given that in a cube of a crystal $$A$$ atom is placed at every corners and the atom $$B$$ atom is placed at every center of the face.
$$\therefore$$ the atom $$A$$ has the contribution of $$\frac { 1 }{ 8 } th$$ contribution and there are $$8$$ corners,so the total number of atoms of $$A$$ are $$\frac { 1 }{ 8 } \times 8=1$$ and $$B$$ has $$\frac { 1 }{ 2 } \times 6=3$$,As the contribution of $$B$$ on each face is $$0.5$$.
$$\therefore$$ the formula of the compound is $$A{ B }_{ 3 }$$