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.