Cardboard box

Peter had square cardboard. The length of the pages was an integer in decimetres. He cut four squares with a side of 3 dm from the corners and made a box out of it, which fit exactly 108 cubes with an edge 1 dm long.
Julia cut four squares with a side of 2 dm from the corners of the same cardboard and created a box. He wants to put cubes with an edge of 2 dm in it. How many cubes will fit in Julia's box?

Correct result:

n =  16


V=108 13=108 dm3 c=3 dm  V=a2 c  a=V/c=108/3=6 dm x=a+2 c=6+2 3=12 dm  c2=2 dm  a2=x2 c2=122 2=8 dm V2=a22 c2=82 2=128 dm3 V3=23=8 cm3  n=V2/V3=128/8=16

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