How to translate objects away from an empty? Is there a way to simultaneously translate objects away from predefined object, so basically all objects will move away from it in radial fashion? 

So, let's say we have an empty in the middle, and some cubes around it. I would like to move the cubes away from the empty, just like in an explosion. I don't want to use particles and force field, but controlled, keyframed animation.

I tried to parent all cubes to the empty, but the only thing I can do is to scale or rotate the objects.
To disable the scale of children objects, you need to add object constraint Limit Scale to each one of those objects. 

In the object constraint enable minimum and maximum on all the axes and change them to 1.

Once you resize the parent object, the position of the child objects will change relatively but the size will remain the same.