(In order of the ____ spaces)
1.) First, find the volume of the cube with a side length of [tex]\frac{1}{3}[/tex] of an inch. [tex]\left( \frac{1}{3}\right)^3 = \frac{1}{27}.[/tex] Then, find the volume of the [tex]\frac{1}{6}[/tex] side length cube. [tex]\left( \frac{1}{6}\right)^3 = \frac{1}{216}[/tex]. Next, divide. [tex]\frac{\frac{1}{27}}{\frac{1}{216}}=\boxed{8}[/tex] cubes that need to fill the cube.
2.) Using the same logic, we get [tex]\boxed{27}[/tex].
