We have a Roku TV that we have connected to our cable service.
We thought we'd eliminate the cable service and switch to Roku instead.
That only happens if the cable provider offers a channel for Roku devices that provides that functionality. If the channels are not encrypted, then you can probably just tune them like a regular over the air TV channel. However, it's very unlikely those pay channels are unencrypted over the cable. That way they can force you to rent a cable box from them, so they can make more money, along with selling your viewing habits to data compilers.
I just searched the channel store for anything from Cox, but it doesn't look like they offer one.
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