Can you solder without flux?

Not reliably, though most people are already using flux without realising it. The overwhelming majority of solder sold for electronics is "rosin-core" or "flux-core" — the flux is a thin core running through the middle of the solder wire itself, so it's applied automatically as the solder melts. If you're using that kind of solder, you already have flux in the joint even without a separate bottle or pen.

Where you genuinely need extra flux is on surfaces that are oxidised, dirty, or already been soldered once and gone dull — a fresh dab of liquid or paste flux there helps the solder wet and flow properly instead of beading up or producing a grainy, weak joint. Soldering with no flux at all, on a clean fresh joint with flux-core solder, still generally works; soldering with genuinely zero flux on an oxidised or previously-worked joint usually doesn't.

See should I put flux on the tip of my soldering iron for where flux does and doesn't belong, and can I use vaseline as flux for a common substitute question.