$A$ child is playing with building blocks, which are in the shape of cubes, and has built a structure as shown in the figure. If the edge of each cube is $3 \, cm$, find the volume of the structure built by the child. (in $cm^3$)

  • A
    $420$
  • B
    $415$
  • C
    $405$
  • D
    $410$

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