Cardboard box

Peter had square cardboard. The length of the edges 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 precisely 108 cubes with an edge one 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 answer:

n =  16

Step-by-step explanation:

$$\begin{gathered} V=108\cdot 1^3=108{\text{dm}}^3 \\ c=3\text{dm} \\ V=a^2\cdot c \\ a=\sqrt{V/c}=\sqrt{108/3}=6\text{dm} \\ x=a+2\cdot c=6+2\cdot 3=12\text{dm} \\ {c}_2=2\text{dm} \\ {a}_2=x-2\cdot c_2=12-2\cdot 2=8\text{dm} \\ {V}_2=a_2^2\cdot c_2=8^2\cdot 2=128{\text{dm}}^3 \\ {V}_3=2^3=8{\text{cm}}^3 \\ n=V_2/V_3=128/8=16 \end{gathered}$$

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