A rectangular prism is completely packed with 180 cubes of edge length 1/3 inch without any gap or overlap

Given the cube has a length of 1 over 3 in. The volume of the cube was:

V=length*width*height

v=1/3*1/3*1/3

V = (1/3) ^3

V=1/27 in^3

thus the volume of the prism will be given by:

volume=[volume of cube]*[number of cubes]

volume=1/27*180=6 2/3 in^3