I recently recorded 16 different songs of the same band using the same inputs, same mics, same everything.  We just set up, got the sounds we wanted, and recorded several different songs with that same setup.  Now that I've mixed the first song, I'd like to save all the settings of that song (fader positions, pan positions, plugins on each track, etc.) and then load those same settings into the rest of the songs since the mixes should end up being pretty similar.  Is there any easy way to do this?  So far I just wrote down all my settings and have been copying everything manually which is taking quite a long time.

Track Templates should do the job or for you project templates might be better. 

The problem with templates is you can't apply them after the fact to a project where the tracks have already been recorded. I think the best option is:
 
1. Open the project with the desired mixer settings.
2. Delete all the audio and "Save As" a template or project.
3. Open the new project you want to mix, and render each track from 00:00 to the end as a WAV file.
4. Close the project, open the template, and drag the WAV files into the template to the appropriate tracks.

Anderton
The problem with templates is you can't apply them after the fact to a project where the tracks have already been recorded. I think the best option is: 1. Open the project with the desired mixer settings.2. Delete all the audio and "Save As" a template or project.3. Open the new project you want to mix, and render each track from 00:00 to the end as a WAV file.4. Close the project, open the template, and drag the WAV files into the template to the appropriate tracks.

I'm not sure about steps 3 & 4. Isn't it possible to just open the original project and the project template and then copy/paste all audio clips from the project to the template?

Forget the templates,  just save the song(s) and name them something like "Song 1 settings".  Now when you want to use the same settings, bring up the song and remove the audio and just start recording again.  You can use "SAVE AS" to provide a new name to the new song with the newly recorded audio. (This is similar to what Scott said)
 
Peace