Is there any problem with your internet connection? Any gate keeper application like little snitch, that could prevent the download of the additional contents? Then deactivate these utilities while trying to download the loops.
Sometimes the additional contents has been downloaded successfully, but GB could not write the Loop index. Try if reindexing your loop library will help, see:
If rebuilding the Loop index does not solve this, backup your system and then uninstall GarageBand and reinstall it, see Dagon's post for a complete deinstallation of GarageBand: Re: GarageBand '11 won't download additional loops
Basically you need to remove the following folders in addition to the GB application:
- Delete the /Library/Application Support/GarageBand folder
- Delete the /Library/Audio/Apple Loops/Apple/Apple Loops for GarageBand folder
To reinstall: Since your Mac is new, GarageBand probably came preinstalled and you do not have installation DVDs. You can download GB again from the App Store, if you accept it to your AppleID.
You have to accept the iLife Apps, before you uninstall them.
- Double-click the App Store icon in the dock.
- Enter your Apple ID and password.
- Click Purchases.
- If you haven't previously accepted your bundled iLife applications within the Mac App Store, you should see your iLife applications appear in the Accept portion of the screen. Click Accept.
After accepting them, you can reinstall them free of charge from the "Purchased" tab of the AppStore,
After a reinstall of GB you should be able to start the download of the additional contents again by launching GB and selecting one of the missing loops in the Loop Browser.
Just in case I misunderstood your question:
When do you get this error message: Directly after launching GarageBand, before you can do anything with it, or when you are trying to add a loop or new track?
If the problem occurs right after launching, try HangTime's "oddball problems" fix first, before going to all the trouble of reinstalling: See the FAQ:
(Let the page FULLY load. The link to your answer is at the top of your screen)