First, we can determine in simple conversion between meter and millimeters. As the prefix tells us "mili". The difference between then is 1000, so
1 meter= 1000 milimeters
Because the value is a volume and not a unit of length, we have to cube both sides.
(1 m)^3 = (1000 mm)^3
1 m3= 1000000 mm3.
The fraction is 1000000 mm3 / 1 m3