First, we know that the cubes are identical, therefore, they would have half the combined volume.
Each cubes's individual volume is 250/2 = 125 cubic cm
Since we know that this shape is a cube, we also know that all the dimensions of a cube are equal.
v=s³ where v is the volume and s is the side length
125 cubic cm=s³
∛125=s
5 cm=s
One of the cube's edge dimensions would be 5 cm.
Hope I helped :)