> Will any ADSL modem router also work as a router when connected to a
> cable modem, presumably via one of the ethernet ports? If not are there
> some that do or which also have a cable modem ethernet input?
No, an ADSL router routes between the ethernet ports and the ADSL modem.
The connection between the ethernet ports themselves is simply a switch.
You require an ethernet router. This routes between the several (usually 4)
ethernet ports which comprise the Local network (labelled LAN), and the one
(or possibly 2) ethernet ports which connect to a cable modem (possibly
labelled WAN)

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Graham J