Nicolas Cage Back for More Karaoke, Trying to Make 'Purple Rain' His Anthem

Something about "Purple Rain" speaks to Nicolas Cage's soul, because he hit up the same karaoke bar twice in 3 nights for 2 emotional renditions of Prince's hit ... which is now Nic's anthem.

We got this new vid of him pouring it all out on stage at what's clearly his favorite joint in L.A.'s Koreatown, and this time around it's way more over-the-top, angry and demonstrative than the first clip we got earlier this week.

This performance went down last Friday, and you see Nic pacing around the room during what we'll graciously call ... his impassioned delivery of Prince's classic. We gotta say, he really went ALL out this time -- especially compared to his Sunday night gig.

Seems he toned it down a bit for the encore, but ya can't blame the guy for pouring his heart into the microphone ... he's going through some stuff. As we told you, Nicolas is trying to annul his recent quickie marriage of 4 days.

Some people pay $200/hr for a psychologist -- Nic prefers free karaoke therapy. Well, plus the cost of drinks, we're presuming.

Nic quickly soured on his new wife, Erika Koike, and filed for an annulment. He says they were bombed when they got hitched in Vegas and it was just the spur of the moment. There were signs the union was doomed ... Nic and Erika were fighting before AND after they tied the knot.

Erika sees it another way ... she claims their marriage still counts and she wants his spousal support.