Unfortunately, the Galaxy Note 3 is among the devices that will no longer receive official updates. Of course, that doesn’t mean the latest Android updates can’t smoothly run on the mentioned device; it is just a marketing decision that’s not based on the Note 3 performances. So, of course, Android 6.0 Marshmallow can smoothly run on the Galaxy Note 3, so why not enjoying the same firmware? If you do want that, then you will have to complete a dedicated update procedure which will be explained during the following guidelines.