Ionic radii of cation A ^ + and anion B ^ - are 102 and 181pm...

In given ionic compound anions form CCP lattice, And cation is present in octahedral void. Means this structure is similar to structure of NaCl. Which is also called rock salt structure.

Edge length = $a = ?$

In rock salt structure cations and anions are in contact along the edge of the cube.

So, $a = 2\left({r}_{+} + {r}_{-}\right)$

$a = 2\left(102 + 181\right)$

$a = 2\left(283\right)$

$a = 566pm$