Top n Bond should be able to handle that for you. Just be sure to spend a goodly amount of time on the surface prep to make sure you remove any loose concrete, dust, paint and anything else that might interfere with the bond (since it is around the pool, I would flood the area with fresh water a couple of times to remove any residual chemicals as well).
After you resurface it, a good quality sealer should help keep it that way. Although I don't recall seeing a specific article on the matter - almost all the spalled concrete I have ever fixed in the past was painted...so if nothing other than superstition, I would probably use a pigment or stain on the concrete instead of paint.
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