Print only part (fraction) of a model
The latest version of Ultimaker Cura can do that (version 3.6).

I have built models made of different material in the same model.

How to do this is:


Select your CUBE and select the icon "Per Model Setting" in left side menu.
choice "Normal model", select the following settings: Top/bottom thickness, wall thickness and infill percentage
Very Important: all above settings must be set to 0!
Select the model you desire to print and select the icon "Per Model Setting" in left side menu
choice "Modify settings for overlap with other model" and select the following settings: Top/bottom thickness, wall thickness and infill percentage
Select the desired infill percentage and the wall top/bottom thickness for the portion you want print
slice the model


Note: If you need to print supports, then in step 2 select "Modify settings for infill of other models" (instead of "Normal Model"), and in step 6 also select "Add Support" and any other support related parameters you may need. However, Cura needs at least one "Normal Model" to slice, so to fool it you need to also another Cube as "Normal Model" with the parameters of step 4 somewhere else in your build plate (it won't really print).