Some people might need to remove part of the trim around your CD player, or the CD player (as I did) in order to remove the cubby. Some of the cubbies have a ledge that slides under the edging of the CD player. Mine does, but Eran's doesn't for example.
Your CD player install kit should have come with several pieces of black plastic trim to install. Some people might have installed theirs to be flush with the outside of the dash, some might be set back a little deeper into the dash.
This is how mine looked like before. You could not remove the cubby because the trim on the CD player hung over the lip of the cubby.
Then I removed that outside piece. Now the CD player is recessed into the dash slightly as compared with the previous more flush mounting. You can now see the edge trim on my cubby though. Erans is installed the same way, but it does not have that outter lip on the cubby like mine does. I'm not sure why there is a difference. Without that trim piece the cubby can easily be removed.
When I remove the cubby, this is how it looks now. As you can see that is the way the trim looks around the clock.