Can you connect both DVI and D-sub cables to the same monitor?

By D-sub, it is safe to assume that it will be a VGA connector on a high density 15 pin D connector.

DVI is normally a digital video signal although it can also carry analog VGA signals as well. Some monitors and projectors will be able to accept both signals as two separate inputs, others may only accept digital DVI connections.

For those that accept analog on the DVI, they may also have a dedicated VGA connector as well. Better monitors will treat that as a separate input to DVI analog so the input selection should offer three separate inputs in that case. Some monitors may only have a single VGA input which may be fed from the DVI analog links and the VGA input at the same time. If this is the case. the DVI input should only be a digital feed if the VGA connector is in use.

The best advice is to check the monitor's user manual and see exactly how the inputs are arranged. If it's not clear, talk to the dealer or the manufacturer. Because all monitors and projectors are designed a little differently to others, it is impossible to offer a definitive answer here.