It will work if you put that 8/3 wire on a 40 amp breaker.
For example the next sub panel I'm going to put in is a 100 amp 12 space square d QO panel. It's going to be connected to the main with emt conduit since they are only going to be 18 inches apart.
I'm probably going to run this 100 amp panel on 6 gauge with a 50 amp breaker. Since its only going to have 6 circuits on it, bed rooms, living room, bathroom, hall way, split A/C unit type stuff. So 3 little circuits on a 60 amp breaker is going to be way over kill.