Gradle sync failed access is denied in android studio
Very late answer, but I was getting the error "caches\5.1.1\file-changes\last-build.bin (Access is denied)", deleting that file and re-building the project worked for me.
In my case, I hid the .gradle file. On unhiding the file, it was fine.
Goto File -> Invalidate caches / Restart
Shutdown Android Studio
Rename/remove .gradle folder in the user home directory
Restart Android Studio (It will download gradle metadata and data)
Gradle build succeed
Rebuild project. Done.
EDIT
Try this for Mac OS
Go to SDK manager (with Administrator rights), scroll down till the end, download "Android Support Library".
And it works (don't forget Administrator rights).
Reference this SO Question..
If do you have an antivirus software, try to check if it has blocked Android Studio.