Depends on turn-around time for title search, any inspections, and/or survey (if applicable).
Typically, in my area an all cash deal can be closed in 3 weeks or less. I have experienced transactions where the closing was 7 days or less from contract. Closing cost should be significantly less , again, depending on charges for the above mentioned items, plus the cost of the closing agent to conduct the closing. You will also have recording fees if you are purchasing, which need to be taken into consideration.