Single connection 2+ cable devices with splitter
In principal, yes you can do this.  Practically, there are some design considerations that need to taken into consideration in order to get the best performance.

There is signal loss every time you split the cable. So first and foremost, the incoming signal strength needs to support the number of devices and splitters over the distance of the cable (longer cable = more signal loss).

When both cable modems and TV are used, often the signal is split closer to the source and a direct feed is provided to the cable modem.  Some splitters have different loss levels for each connection and this is also used to provide higher signal strength for longer or runs or internet modems.

You should also contact your provider to ensure you can do this on your own.