Ok what you need is not a group, but a hierarchy.
A group is there to share visibility, selectability and rendering properties to all their members.
On the other hand, a hierarchy is there to carry transformation, animation and similar kind of properties from one object to others. Basically, you apply a transformation to the parents, and it is carried to the children.
To achieve this, create an object that you will animate (rotate, in your case). The best object you can use for this is a null. Place the null at the location you want the rotation axis. Deselect it, and select all the objects that you want to rotate, click MCP > Parent, and pick the null with the middle mouse button. Now all your boxes are children of the null.
Then select the null and rotate it.
Tip: In the Constrain menu, uncheck Auto Child Compensation.
Hope this helps
Salutations - Cheers
Bernard Lebel