I found: ##243mm##
Consider the cube of side length ##x##. The volume will be equal to ##x^3##.
So if we have the entire volume ##V=27^5## we can take the cube root of it to get the side length:
##x=root3(27^5)=243mm##
To check it we can try:
##V=243^3=14348907mm^3=27^5mm^3##