If you're developing the full system then no, don't include the DB as an Actor. I wouldn't recommend showing the Server either.
The purpose of a UCD is to show the system context in terms of the features (Use Cases) it supports and for whom those features are provided (Actors). UCDs deliberately don't show internal structure - so you focus on the Users and their Needs without getting sidetracked by implementation concerns.
Since the Server and DB are part of your system they're "design detail" for how you realise the Use Cases. Therefore the don't sit outside your system, therefore they're not Actors. The only time I'd recommend putting other systems on a UCD is when (a) they're external to the system you're building and (b) provide or receive some value to/from it.
UML provides other diagrams for showing the internal components of the system:
- Deployment diagrams show physical hardware and allocation of software components to them
- Component Diagrams allow you to show the logical structure of the application
- Sequence Diagrams or Activity Diagrams allow you to show how a Use Case is realised in terms of its logical components
(Note I'm not suggesting you use all those, just what's useful).
hth.