The Samsung Galaxy Note 8.0 launched with Android 4.1 instead of 4.2 like the Galaxy Tab 3 8.0 did, but if you want you can flash a leaked version of the official 4.2.2 update. While the update is not rich with new features it reportedly makes the tablet smoother and improves battery life.
The bigger Note 10.1 (which launched with ICS) is still on Android 4.1, so the newer tablet will actually get ahead.
Anyway, you can grab the RAR file you need for the update here, the file is about 1.2GB big. Note that this firmware is for the N5110, the Wi-Fi only version of the Note 8.0 and will not work on the 3G/4G-enabled N5100.
You’ll need Odin 3.07 (it’s included in the file if you don’t have it already). Follow the installationinstructions over at SamMobile and keep in mind that the process will wipe your data, so make a backup first.