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Hi, I'm Mike G and I'll be assisting you. Let me advise you that not using a PVC conduit would be a mistake. Ground conditions over a period of time could cause a failure. You'll need to envelope the feeder in 6 inches of sand if you don't use a conduit. The cost and the labor more than justify using conduit. Having said that, how long is the run? What size service is in the house?
I ran the calculation and to have a 60A feeder you would need a 500MCM Aluminum wire. It may be better to install a transformer at each end to reduce the wire size. Using a pair of 480V transformers will reduce the wire size to 4/0 Aluminum. A quad URD cable either in or not in conduit is the wire type.
Very good, you're welcome.