Does Google App Engine support Java 8?

Not at the time of writing but you can keep track of the status in this issue:

• Java 8 support: https://code.google.com/p/googleappengine/issues/detail?id=9537

Java 8 is now generally available on App Engine Standard Environment, joining the GA runtime on the App Engine Flexible Environment.

Learn about the differences.

The new Java 8 runtime has all the benefits of Java 7 but with upgrades and enhancements:

• OpenJDK 8-based Java runtime supports the standard public Java library (no whitelist)
• Doesn't impose a security manager--your code won't be restricted by Java permissions issues.