A cubic metre is a HUGE volume. And $1*cm^3-=1*mL=10^-3*L$. These are all common units of volume in the laboratory. In Europe, we buy milk in litres, and in England, sometimes we buy milk in $"pints"$, $600*mL$.
$1*cm^3=(1xx10^-2*m)^3$. Why? Because the prefix $"centi"-=10^-2$. And thus............
$1*cm^3=(1xx10^-2*m)^3=1xx10^-6*m^3$.
Sometimes I remember that $1*m^3$ (which is a HUGE volume!), is $1000*L$, and that there are $10^3*cm^3$ in a $L$. An equivalent term for the $"litre"$ is $"cubic decimeter"$, $dm^3$.
And thus $1000*L=10^3*Lxx10^-6*m^3=1xx10^-3*m^3$.
Equivalently $1*L=1*dm^3=(1xx10^-1*m)^3=10^-3*m^3$, as required.
It is worthwhile getting your head around these problems. If there is an issue you want further clarified ask away, and someone will help you.
