Answer
$0.001\ cm^3$
Work Step by Step
We know that there are 10 millimeters in 1 centimeter. Using this, we find how many cubic centimeters are in a cubic millimeter.
$1mm^3=1mm^3\times(\frac{1cm}{10mm})^3=1mm^3\times\frac{1cm^3}{1000mm^3}=\frac{1}{1000}cm^3$