I want to be able to play the cable tv audio through the receiver.
If using HDMI from your cable box to the receiver and then to the TV works, then you'll get cable TV audio through the receiver.
If, as is sometimes the case, HDMI fails to operate reliably, then you might need to fall back on plugging it directly into the TV and routing audio differently. This could be from the television either via ARC or optical or coaxial SPDIF. It could also possibly be from an SPDIF or other audio output on the cable box plugged separately into the AVR. It's a matter of finding what works best with your particular setup.
Be aware that the kind of lossless mutlichannel audio streams supported by Blu-Ray will not 'fit' into SPDIF, but Dolby Digital will, which is as much as you probably get via cable.