Note: the OPs stated modem mode,l Arris TG826G, does not seem to exist, The available documentation of the Aris TG862G is quite skimpy.
A Packet Sniffer program, such as Wireshark (free at wireshark.org), can capture all traffic when the computer it is on connects to a network. If the computer is connected to a Router, only traffic between the Router and that computer is available. This is because a Router directs traffic only to the computer that the traffic is addressed to.
To see/capture incoming and outgoing data on the whole network, you need to connect between the Router and the MODEM. This is typically done with a device called a Switch, which has multiple ports to connect to computers, modems, and Routers. A Switch reads its ports and everything coming into it is repeated to all the other ports. Think of it as a splitter or copy machine. Four and five port Switches are common with prices starting around $15.
Addendum
There MAY be a way to load capture software onto the Arris MODEM/Router. Perhaps someone more familiar with the details of the Arris can contribute something here.
end Addendum
Unfortunately, your MODEM, Arris TG826G TG862G, is a combination MODEM and Router so you can't connect between them. You would have to turn off the wireless function on the Arris, wire the Arris to a Switch, wire a new Router ($50 and up) to the switch, and wire a computer with Sniffer software to the switch. Notice the need to wire those together.
Once all of that is done you will be able to see the numeric IP address of all incoming and outgoing communication; including the DNS requests for named URLs (the online lookup that reports back the numeric address for named addresses).
Since everyone is concerned about privacy these days, most content is encrypted so you won't be able to read messages, etc. Some older encryptions are 'relatively' easy to subvert given enough data. How to do so is beyond my knowledge and probably not something that could be posted here anyhow.
Since each device that connects to the Internet has its own unique address, that's how you can track what is connecting thru your network. Of course then you have to find the actual device that has that unique address.
Cheers,
Tom