I was wondering if we can submit sitemap to Google for forum also? Will it work to index all posts in Google?
Google doesn't particularly care if your website has a forum. A forum should always have a sitemap, and Google should have no problem picking up your posts.
Why I asked this question because forum has dynamic content all the time so it wont be any problem in submitting sitemap again and again?
You don't need to repeatedly submit it. Set up a Google Webmaster Tools account and link to your sitemap from there.
It will work ... but this doesn't mean that you will see them in cache. You should know that google index much more then it shows in it's results.
You can open an account on Google Webmaster Tools so that you can link site map with it helps.