How to install Android 5.0.2 Lollipop on Nexus 6.
Google's Nexus 6 is the first Nexus smartphone to come pre-loaded with Android 5.0 Lollipop. While Google has already issued the first update to Lollipop software incorporating the Android version 5.0.1, the next update, Android 5.0.2, which is already available for Nexus 7 2012 Wi-Fi, is yet to make its way through the new Nexus smartphone.
Interested users can still update their Nexus 6 to the latest Android software 5.0.2 ahead of the official roll-out, using the customised official CyanogenMod 12 nightly, launched recently. Needless to say the CyanogenMod operating system carries the features and customisations which are unavailable in the stock Android firmware.
So if you want to try out the new CyanogenMod 12 nightly build on your Nexus 6, head over to the following installation guide.
Pre-requisites
  • As the tutorial might wipe out all data of the phone, create a backup using any custom recovery.
  • Enable USB Debugging Mode on the phone to connect it with the computer and use Android SDK with it. [Go to Settings>> About phone. Scroll down to Build number, Tap seven times on the build number. The Developer options under Settings should appear now. You can now enable USB debugging mode.]
  • Your Nexus 6 should have above 80% of battery charge.
  • The phone should be rooted and have latest version of recovery installed.
  • The bootloader of the phone should be unlocked.
  • The CyanogenMod 12 nightly works only with Nexus 6 codenamed Shamu. Applying these on any incorrect variant might brick the device. Verify the model number of the smartphone by navigating to Settings>> About phone>> Model number and install firmware accordingly.
  • Since this is a nightly release, you might not get all the features working.
  • IBTimes UK will not be held liable for any damage to the device. Installation will be completely at your risk.
Download files
CyanogenMod 12 ROM: cm-12-20150115-NIGHTLY-shamu.zip [or, here] 
Gapps file [or, here] 
How to install Android 5.0.2 on Nexus 6 using CyanogenMod 12 official ROM
Step-1: Connect your Nexus 6 to the PC. Without extracting move the downloaded files to the internal storage of the phone. Now Unplug the USB cable from the phone
Step-2: Power off your Nexus 6 and put it into recovery mode
Press and hold Volume Down, Volume Up and Power buttons together
Release all three buttons when the Fastboot Mode menu appears
Use the Volume buttons until the upper part of the screen shows Recovery Mode text
Press the Power button to select Recovery Mode. You should see an Android icon on the screen. Now press Power button then Volume Up
The Recovery Mode should appear now
Step-3: In the recovery mode, create a Nandroid backup of the current phone set up
For CWM: Select backup and restore
For TWRP: Select backup
Give a name to the backup file and confirm the process
Step-4: Perform factory reset. Keep in mind this process wipes all data that has been installed on the system memory using the previous ROM. But it will not delete anything from internal storage of the phone.
For CWM: Select wipe data/factory reset
For TWRP: Select Wipe option
Step-5: Flash the CM12 ROM
For CWM: Select install zip from sdcard>> choose zip from sdcard
For TWRP: Tap on Install
Browse to the folder where you have saved the CM12 ROM, select it and confirm installation
Step-6: When the custom ROM is installed, repeat the similar procedure to install Gapps file
Step-7: Finally reboot the phone to normal mode, after all the files are installed
Note that rebooting the Nexus 6 after the ROM installation will take some time. So wait until the process is completed
Your Nexus 6 should now be up and running on the customised CyanogenMod 12 firmware with Android version 5.0.2.
[Source: Android Geeks]