Check an HD movie channel, or at least some channel playing a movie.
It should be broadcast in at least DD5.1, if not DD Plus 5.1, and you will definitely hear LFE if the track is getting sent.
Most broadcast TV has low bitrate audio, and minimal LFE.
Even a primetime TV show in HD and 5.1 has pretty weak 5.1 compared to streaming services.
I've compared my recorded episodes of Under the Dome to the episodes on Amazon Instant Video - and Amazon blows the cable recordings away. I set my volume much lower on Amazon, and the LFE alone is far more visceral (and it's still only DD5.1, not a lossless codec). Cable audio is definitely quite low bitrate.
Now, if you confirm 5.1 broadcasts are at least using some LFE, then it's probably just an issue with very low quality audio on other channels/shows, or something.
If you don't get anything at all from cable, check your cable box menus. You may need to force Dolby Digital Out within the menu.
Since the sub obviously works, it's not an issue on the sub itself or on the receiver (at least, not likely). It seems as if any audio properly coded is getting sent where it should.
I highly suspect a setting needs be toggled somewhere within the cable box menus. Just connecting using the proper cables doesn't always trigger the correct automatic settings.
When you say digital audio cable, what is it you are using? HDMI? Optical? A cable with a single RCA-style connection on both ends?
If it's not either of those, you probably won't get 5.1 at all from cable.
If it's not HDMI, you almost definitely have to get a setting configured correctly on either the cable box or the receiver.
Some receivers cab be tricky with cable sources, in that cable isn't always 5.1 so you may or may not even want only direct input. Some people may want simulated surrounded when real surround is not present, and it seems some receivers almost always default to such a setting when detecting mixed inputs (since most commercials will be stereo even if the show is 5.1).
Have you ensured that all other speaker channels are getting audio when watching cable? Or, have you only looked into the LFE track issue? I.E. when you aren't hearing LFE, are you still getting and hearing rear and/or side channel tracks?