Take it to a DIY car-wash, drop a few quarters, and power-wash that sonofabich. Probably cheaper than buying acid or even a brush or whatever.
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Awesome! There's one closeby that's locally owned, doubt the owner would mind. Only question is if it would damage the cinderblock at all with chipping or whatever.
It's not chipped, those are premium beveled edges!
Step one: soap and water. Step two, a mild acid -- you probably have a citric acid based bathroom tile cleaner already or similar. Wrap it in a sacrificial towel or similar and let it soak in that weak acid overnight.
Because you don't have a driveway/hose, I would try something like the Simple Green "OxySolve" cleaning concentrate (it says it's for power washers but there are mixing instructions for "manual cleaning"). Most concrete cleaners have some pretty harsh chemicals in them that could damage your bathtub, but the Simple Green stuff seems pretty tame.