Identical charges (–q) are placed at each corner of a cube of side 'b' then electrical potential energy of charge (+q) which is placed at centre of cube will be

The distance from the centre of a cube of side b to any corner is half the body diagonal: $r = \dfrac{\sqrt{3}b}{2}$.
There are 8 corners, each with charge $-q$, all at the same distance r from the central charge $+q$.
Electric potential energy $= 8 \times \dfrac{1}{4\pi\varepsilon_0}\dfrac{(q)(-q)}{\sqrt{3}b/2}$
$= -\dfrac{8 \times 2q^2}{4\pi\varepsilon_0\sqrt{3}b} = -\dfrac{4q^2}{\sqrt{3}\pi\varepsilon_0 b}$
So the potential energy of the central charge is $\dfrac{-4q^2}{\sqrt{3}\pi\varepsilon_0 b}$.