The conversion only gets tricky with the cubed labels. Keep in mind that cm^3 is cm*cm*cm, and that m^3 is m*m*m, AND that there are 100 cm in 1 meter. Here's how the conversion will look if we expand it to make it simple to understand:
. If we do all that multiplying and dividing, and all the crossing out of the labels that cancel, we get
. There you go!