By upgrading from 6.1.4 to 6.1.6 mods will work

I want to upgrade my site from 6.1.4 to 6.1.6.

Whether the mods which I have at present - 7 colour templates, inviter,google search & adsense - will work in 6.1.6 or not.

Well, most probably they would work as 6.1.4 and 6.1.6 are not much different.

What you will need to do after upgrade is to reinstall these mods to check if some of the code of these mods has gone missing.

Most mods are modifying core Dolphin php files with instructions like "go to line X and insert these lines: xxxxx". Since many files have been changed from 6.1.4 to 6.1.6 there is a chance the mod installation instructions will have to be changed. I suggest 1) checking that none of the files modified by the mod has been changed in the upgrade or 2) contact the developer of the mod.