you need other hardware, but
channels does what you want.
You need a network based tuner, I use the one from HDhomerun with a cable card, so I get most of the cable channels on it. It has 3 tuners that all work from the same card.
You need to do a bit of research about your cable company and copy protection flags though, it will depend on how they have them set. I get pretty much everything but the HBO family, and Fox family (various "news", and nat geo), which sounds standard, but other companies might have more flagged so that you can use them. (google your company and "cci flags" to figure it out)
The tuners are also compatible with unscrambled cable channels (plug your cable directly into the TV to see what you can get) or antenna
with just the tuner, and the channels app, you can watch and pause liveTV, and it has a nice guide also.
With their subscription ($8/mo, $80/yr) you add full DVR capacities.
You will need a computer running, but it works on Win, Mac, and linux. They also have a raspberry Pi image. And it runs on several NASes also.
with that you get a full DVR, with all the basic features.
it's whole house, so all of your front ends connect to the same bank of tuners and recordings.
also with the subscription, you get remote access, so you'll be able to access from anywhere, as long as you have a decent internet connection.
they also use a service called TV everywhere, which takes your cable login info, and adds all the streams you have access to. They then show up just like a regular channel. It should be possible to run it with just this, and no tuner box, but you should confirm. (must have subscription to use this feature)
They have front end apps for most devices - aTV, fire stick, android, and iOS.
it also works in web browsers.
you say cable is included, do you have to rent the boxes? or are they included also.
with fios I pay $5/mo for the card (for 3 tuners that work on every tv with an aTV), while set top boxes are $12 for each TV you want to watch on.