C182 Flight Instructor reported nose gear indication did not illuminate during gear extension. Reporter returned to departure airport and landed with nose gear retracted.

Narrative

After working with the student at ZZZ1; on the last trafic at ZZZ1; I was going to ask for a go arround; on the downwind; he was doing the checklist and when he lower the landing gear we did not saw the nose landing gear indication in green; at this point ZZZ1 Tower was closed and we decided to return back to or home airport ZZZ. We raised the landing gear; depart the ZZZ1 airspace and cruise to ZZZ. When we arrive to ZZZ we put the landing gear down and we did not see the light indication so we ask Tower to do a Tower fly by to be sure about it. Tower confirm it and we ask to go out of the airspace to perform the emergency checklist for gear not comming down. We cicle it again and no change; so we used the emergency pump; puming around 40-50 times and still no indication of the landing gear coming down; so we decided to execute a high positive g 60-50 deg turn and see it this would unlock it; from va to close first stall indication. This did not unlock it. We came back to ZZZ airspace and advised ATC; at this pont we run the chack list again just in case we miss something and also call the safety officer of the club (he is way more experience than us and he could also help with his experience and information on ground) we open the gear circut bracker and pump the emergency handel 40-50 times and still nthing; so we close back the landing gear breaker and pum it 30-40 times; with the same result. After that with 40 gal of fuel (approximately) we told the Tower that we were going to land afer 1 more la to set up our selfs; I was going to take controls for the langing and; with seat belts tight; on fina we were going to open the doors and we were aiming to perfrom a 'soft field type' landing. On the flare and close to touch down we I will give the call to kill the electricals power and mags; and I will be in charge of pulling the mixture and holding the nose out of the ground as much as possible to slow us down as much as we can. Once stopped; we both egress the arlane that was still close to the middle of the runway; no smoke or fire came from it and no injures on both occupants; the emergency team came to the airplane and inspect the airplane and ask how we were. (all landing gear swings in the air were between 80 to 90 kts.)