Volume of cuboid = 60 cm × 54 cm × 30 cm = 97200 cm^{3} Side of the cube = 6 cm

Volume of the cube = (6)^{3 }cm^{3} = 216 cm^{3} Required

number of cubes = = Volume of the cuboid/Volume of the cube

= 97200/216 = 450

Thus, 450 cubes can be placed in the given cuboid.