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Create new empty to rotate cube around

I'm taking "Fundamentals of Animation" Course at the moment. There is a anticipation-exercice that I wanted to extend a bit.. Basically I want to know, how I can add a new Empty that allows me to rotate the cube around, without messing everything up.

I already got a little help from Jonathan, but i still have troubles solving my problem! He said:

 " The thing that is parented to the empties is the Axis object (X/Z empty) , so I was able to get another rotation by adding another child of constraint to a new empty. The tricky part is to Set Inverse at the beginning of the animation and then move the axis to get the cube back into place."

Could anyone explain me how or what I have to set invesere at the beginning of the animation? Or wich Steps I have to take to add a new "Rotation Empty"?

Since I don't know a lot about Parenting, and how childs act to them, it'd be very helpful if you could explain me as detailed as possible :D

Here is my blender file :

Thank you very much for your help and effort!