How can I install a ceiling fan that needs a 4" box where I only have a 3" box?
If the ceiling is concrete, you can mount the fan to that.  Fan boxes are meant to support the fan, but a concrete ceiling will support it just fine.  As long as there's enough room in the box for the wiring, use the 4" fan bracket to mark two holes outside the box on the concrete that won't interfere with the wiring coming out of the box, and use appropriate tools and fasteners to attach the fan bracket to the concrete around the old box.

If you can't modify the box, chances are good, being embedded in concrete, that it'll still hold the heavier load of the fan designed for the bigger box, and you can modify the fan bracket, or use an adaptor.

If none of these solutions seem workable you can buy a 4" box, and mount it to the 3" box, then mount the fan to it.  It's not ideal, as the fan mount would no longer be flush to the ceiling, but it should work just fine, and provide all the room you need for wiring.