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Suppose we are looking at the cubes A, B, C and D from the top:

     AAA
     AAA
    -----
  BBB | CCC
  BBB | CCC
    -----
     DDD
     DDD

The dashes represents the square-shaped surfaces that are touching.
So there are 3 pairs of touching surfaces. They are pairs because
there is one on each side. So total 6 square surfaces.

Each square = 150/6 = 25cm2. So each square has side 5cm.
Volume of each cube  = 5 x 5 x 5 = 125 cm3.

 

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