A solid stands on a horizontal table. Every horizontal cross-section of the solid is a square. At heights of $0$ cm, $2$ cm, $4$ cm and $6$ cm above the table, the squares have sides of $12$ cm, $9$ cm, $6$ cm and $3$ cm. The side length continues to change in the same way all the way to the top of the solid. Find the volume of the solid.

• A$384$ cm$^3$
• B$576$ cm$^3$
• C$288$ cm$^3$
• D$192$ cm$^3$

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