Whatever you do you will eventually get mold if you leave the grout wet.

For this reason I would advocate drying the grout after each use, I know it’s a bore, but it only takes a second or two.

If you’ve gotten it clean (white) and the black comes back within 5-7 days, you have a problem BEHIND the tile. Adding more sealant now won’t stop the mold that’s already in the wall.

If the builder/installer used ‘regular’ dry-wall behind the tile or tub surround, it has accumulated moisture and grown mold. They are supposed to use green-board, which has green paper instead of the white to identify it — it is made of a different combination of minerals that makes it less absorbant.

If you really have mold, the solution is to tear down the tile, remove the soggy drywall, and clean behind. This may even require replacing studs and the wall to the next room or outside. It can be a BIG job.

How to look:
If the tub is on a wall to the next room, go there and remove an electrical outlet box (turn off the power!) and use a flashlight to look into that wall cavity. If it smells bad, it is moldy. Use a screwdriver to poke at the wall that the tile is attached to — if it’s soft, you have mold. If the wall is soft around the edge of the tile, the paint is bubbling, the wallpaper is coming un-stuck — all bad signs.

Mold is a hazardous condition, and can cause illness to you and your family. If you rent, call the landlord right away. If you own the house, check the timeline on your warranty and homeowners insurance. If the builder knowingly used drywall instead of green-board, you ‘may’ have grounds to pursue them for the repairs, etc.

Good luck!

Have you tried using bleach? The other thing which works well is hydrogen perxoide.

That stuff will kill any fungus, if neither of those work yes I would replace the grout.