I need to have a cube (the BLUE one) to be linked to a parent (the RED one). So when I move the RED cube from the ground the BLUE cube shall move in the same direction proportionally.
How to make this kind of link in Blender?
You can give your blue cube a Transformation constraint with the red cube as Target:
Enable the Extrapolate option. In the XYZ fields, choose the values you want, it will determine the ratio. If you choose -10/10 and -10/-10, the blue cube will move as much as the red cube on the given axis. If you choose -10/10 and -20/-20, the blue cube will move twice the distance of the red cube:
Copy location constraint.
Red is parent of Blue. Both at same location.
Blue is given delta location Z to offset it from Red. Could use Z location
A copy location constraint is added to Blue to Map the global Z location of Red to it's local location. Check use offset to use the delta Z location set above.
Note this all works well until the Parent is transformed, at which case the spaces no longer match.