Let
V1 = volume of the smaller cube (with 1/3 cm sides)
V2 = volume of the box shown
The first volume is
V1 = (1/3)*(1/3)*(1/3)
V1 = 1/27
The second volume is
V2 = (5/3)*(4/3)*(2)
V2 = 40/9
Now divide the two volumes
(V2)/(V1) = (40/9)/(1/27) = (40/9)*(27/1) = 120
Therefore you can fit 120 of the smaller cubes in the larger box shown.