It's not usually a dyed speedcube. Force cubes are usually stickerless cubes. You take 6, take apart all the pieces, and rebuild a cube with just one base colour. Much like the black stickered cubes you then end up with a red/white/yellow/blue/green/orange stickered cube. They're pretty neat looking.
IMO, calling them force cubes is generally very confusing. I'd prefer calling them what they are. Non-black, stickered cubes.
An youtuber called AL60RI7HMIS7 did these with Zhanchis at the start of 2012 and send to some youtubers. The term force was used since stickerless cubes had better plastic that lead to better performance and stickerless cubes were still illegal at the time and this was a way to get that better performance on a cube that could be used officially. It a bit like Florian Holes that was taken from the Florian Mod for ShengShou 5x5 back in 2012.
Here some videos from the time. Since then the term stuck.