Laptop speaker not working?

Sound is turned up everywhere, but there's no sound when I record a video.

However, when I plug in the headphones, the sound is there.

What can that be?

Either because you are on mute (the volume changes when you use headphones) or your speakers are broken.

I would say the speakers are broken.
try the Windows troubleshooting

(Usually doesn't bring anything but is worth a try)

This is due to your microphone

Turn your head on: If you are recording a video and there's no sound, then it is more of a problem with the microphone than with the loudspeaker, isn't it? Here, for example, there's a volume setting…