If the guest cancels, the remaining dates will be made available again and a refund (if any) will be calculated automatically. Did you follow different procedures ?
The guest hasn't actually cancelled, simply moved out after the one night to stay with some friends nearby.
Out of courtesy, the guest has been reimbursed with 6 of the 8 nights that were paid for (2 days payment kept for one night's stay, plus extra day against cancellation policy).
The guest did not ask for a refund, it was offered.
Now the room is vacant, but if possible, I would like to see it available again.
@Christopher625 The way this is supposed to be done is: Guest cancels rest of stay. They will then be refunded automatically for unused days according to your cancellation policy. The dates will open up. There is no need for you to send a refund unless you wish to refund them more than they receive from Airbnb after their cancellation.