How many (3 by 3 by 3) cubes are imbedded in a (4 by 6 by 7) rectangular prism?

Question

In a (4 by 4 by 4) cube, there are 64 (1 by 1 by 1) cubes imbedded; 27 (2 by 2 by 2 ) cubes imbedded; 8 (3 by 3 by 3); and 1 (4 by 4 by 4) cube imbedded. How many (3 by 3 by 3) cubes are imbedded in a (4 by 6 by 7) rectangular prism?

Answer 1

6.22

to check,
3*3*3 = 27 cubic units
4*6*7 = 168 cubic units
27 * 6.22 = 167.94

Pretty much the answer is between 6.22 and 6.23. If you want whole numbers it is 6 cubes.

Answer 2

divide the volume of the prism by the volume of 1 cube:

168/27 = 6