Update 2019-05-07: The java8 cask is affected by recent licensing changes by Oracle. There’s a discussion over on github about this. I’m leaving the post up partially for historic context, but the java8 cask is no longer available, at least at the time of writing.

Update II - 2019-05-07: It looks like due to the recent licensing changes, the Java 8 JDK that brew used is not directly accessible anymore and likely behind some kind of paywall. The installation method described below will still work as it uses the non-versioned java cask, which installs the latest version of OpenJDK.