There is a mechanical switch in the DV6 headphone jack that is theoretically supposed to cut sound to the external speakers when a headphone is inserted that can sometimes stick, but that doesn't sound like it is the case in this instance. Beats audio is esentially a rebranded Soundmax audio (IDT) codec style driver, and they are a pain in the **** to troubleshoot when they go bad. There are a couple things to try. For starters, right click on your speaker volume icon down in the lower right next to the clock, and select "playback devices". You should see your headphones and your speakers amongst other things. Unplug the headphones and see if they indicate that they are unplugged, then plug them back in. If the headphone indicator doesn't show the headphones were inserted, you likely have a damaged jack due to an ipod headphone plug having been inserted into your laptop at some point. If thats the case, you're screwed and will have to explore alternative solutions, such as a y joiner into an external audio volume control amp of some sorrt. If it does show the removal and insert, the headphone jack is probably fine, and you may be able to right click on it, set it as the default device, and if necessary disable the speaker output, which should force everything to use the headphone jack.
If that doesn't do the trick, you are likely looking at needing to uninstall the sound driver, reinstall the latest version, and pray that it works. Aside from that, I'd have to see it.