Does Android SDK with API 23 (Marshmallow) supports Java 8?<>
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No, Java 8 isn't supported. What you can do instead to write Lambdas and method references is to include retrolambda dependency to your project. Same with streams, here is a backport library. Alternatively, consider using kotlin.
Android is using the retired Apache Harmony as its Java implementation and I believe Harmony is on Java 6, so no, Java 8 is not supported.
Java 8 will be supported in Android N though as it will use OpenJDK instead of Harmony.