Should you try to advertise or mention your forum on related Facebook groups? If done right, this could pose a good opportunity to get new members who are interested in the same subject as your forum. The only problem might be some could say you are spamming. What are your thoughts on using Facebook groups to promote your forum?
Social media is also effective when it comes to advertising any forum, I haven't used Facebook group but what I think that your group should have lots of members first for better result.
If given the opportunity, take advantage of the promotion. It can't hurt anything. People see it as spam, some though see it as an interesting site worth looking into. If you can get 1 out of 6, awesome!
I actually have some Facebook pages that I encourage people to promote their gaming clans on the page. It allows me the opportunity to use my page and promote the site I have for them to also promote their gaming clan on as well.