Write the relation between ‘liter’ and ‘$cm^3$’

Hint: A liter is equal to a cubic decimeter. Note that, we can easily convert centimeters into decimeters and convert it into liters.
On the other hand, a cubic centimeter is the same as a milliliter. Here we can convert milliliters into liters and find the relation between cubic centimeters and liters.

Complete step-by-step solution:
A liter is defined as a special name for a cubic decimetre or (\[10\] centimeters $\times$ \[10\] centimeters $\times$ \[10\] centimeters) (\[1{\text{ }}L \equiv 1{\text{ }}dm3 \equiv 1000{\text{ }}cm3\] ).
Hence \[1{\text{ }}L{\text{ }} \equiv 0.001{\text{ }}m3{\text{ }} \equiv 1000{\text{ }}cm3\] ,
and \[1m^3\] (i.e. a cubic meter is the SI unit for volume) is the same as\[1000L\] .
To convert between \[cm^3\] and liters, it is helpful to know that a \[cm^3\] is the same as a milliliter\[\left( {mL} \right)\].
\[1cm^3 = 1mL\]
and the relation between \[mL\] and \[liters\] is
\[1000mL = 1{\text{ }}L\]
Therefore the conversion factor between \[cm^3{\text{ }}and{\text{ }}L\] is \[1000cm^3{\text{ }} = 1{\text{ }}L\]

Note: Liter is the derived unit of cubic meter cube and milliliter is the derived unit of cubic centimeter cube.