I used a combination of things to get rid of my GHA, but they might not be applicable to a 15g cube.
The cause of mine was overfeeding. I created a frozen seafood mixture and didn't dilute it enough. The result was elevated nutrients and GHA covering everything in the tank. Most of my corals are trash at this point. Fortunately they were all cheap frags so it's not the end of the world (for me, at least).
First was to do extreme limits on feeding. We're talking one feeding every day or sometimes every three days. I also started feeding flake food for now.
I hand-picked whatever algae I could, which wasn't much.
Next was to start dosing NOPOX to limit my nitrates.
I got an algae scrubber to give the algae a place to grow that wasn't in the tank.
This all stopped the growth. Next was a bunch of tuxedo urchins and emerald crabs. The limited feedings also encouraged my turbo snails to start munching on the algae.
At this point there are only a couple of strands of GHA still holding out. The tank is otherwise void of it.