My M3 SR charges at 30a on a 40a circuit using 8ga NM cable (Romex) wire. Since the SR only does 32a max charging, it's all that's needed. It's the third generation of EV (LEAF, Rav4EV, Model 3) to charge on that circuit and EVSE.
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I just installed a shiny new 14-50 on a 50a circuit. It uses 6ga THHN wire in conduit and could be upgraded to 60a with just a breaker change (and removing the outlet). It charges my Rav4EV at 40a.
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BTW, the answer to your question in the OP is that 6ga wire is fine for a 60a circuit if it's individual wires in conduit, but if you use NM cable (Romex) then it requires 4ga.