Flight instructor reported the aircraft's wheel got stuck in a taxiway crack that had just been tarred over.

Narrative

Aircraft got stuck in Hot Tar covering a significant hole. We got off runway XX R requesting a taxi to run up area to close and open flight plans; as well as perform before takeoff flow and checklist. There was a gap covered in tar on the run up area; we taxied past it; but the student turned the plane and we thought we weren't on that gap. Did what we needed to do; got ready to taxi to the hold short line; and the plane veered left; it stopped. We thought it was just the gap; and added a little power trying to straighten the nose wheel; after a couple of attempts; we called tower and let them know we were stuck. We waited a few minutes; someone came out and told us to shutdown the plane; and we got out. The left main had got caught up in the tar; and the nose wheel was also stopped on the tar; and the planes wheels were sinking into the slight bit of tar covering the gap. We tried with assistance to push the plane slightly; but it was stuck. After talking to the DOM; and then maintenance; the Tucson airport authority had come out with a tow bar attached to a pickup truck. Maintenance said they could tow it; as long as it wasn't too far; they towed it out about 5 feet; and got it unstuck. We performed a visual inspection; other than some black residue on the fairing; the wheels and fairings looked fine; and the plane taxied; landed and took off fine. Called maintenance; squawked aircraft for a pin inspection of the fairings. Also; the caps pin placard wasn't in the plane during our post flight; and it was realized that it had been blown out of the flight deck with the gusting win; as it kept falling down and was barely hanging on to begin with. Included in the squawk to maintenance that new caps placard required.Suggestions: A note be sent out about those cracks; and to make sure you avoid them; and definitely don't park on them.