I need to put a subpanel on the external wall of the house (far end of the house) for feeding many outdoor receptacle circuits for the backyard.

I will initially use it for six 20 Amp circuits. These circuits are very unlikely to be used all at once. I will probably need couple of more circuits in the future.

I think all I need is a 60 Amp rated panel, but I need a lot of circuit spaces. I cannot find a low Amp rated panel with many spaces. It looks like I need to buy a 125 Amp rated one to be able to get a lot of circuit spaces. This is all fine, but the question is the following:

The subpanel will be driven by a 60 Amp double pole breaker. Can I use #6 wires to a 125 Amp rated panel in this case?