"3 x 50 AMP breakers (depends on local codes)"
Each breaker at 240 VAC
"Minimum 3 x #8 AWG Copper (depends on local codes)"
So you'll need at least #8 -- but more likely #6 conductors.
(I'm assuming that you'll be dealing with a 60 degree panel board and or are using Romex. Otherwise, you'd be able to use #8.)
I've never installed such a beast.
Instead I've installed insta-hots 30A @ 208 or 277...
You'll have to deal with line-of-sight disconnecting means -- which normally is addressed by a sub-panel rated 150 Amps @240VAC.
You can pipe and wire the feeder -- or use MC -- they make it big, BTW.
MC is available all the way up to 705 kCMIL. (!)