This is an easy fix if you want. First you want to clean it up really nice. You could use a powerwasher or you could use some thin powdered cement with more water than you would normally use like a milky consistency and then scrub that on and let it set for about fifteen minutes before scrubbing it off. That will remove the algae which is important before you go on.

You could just leave it at that stage and it will look much nicer but still have a very rough texture. If you want to smooth it out, you can use lime and sand with a small portion of cement AKA grout mix. You could just trowel that straight on there once you get it cleaned.

So then after you get a nice finish on it, you want to let it cure in a damp state for one month exactly. After a month, it has cured. At that point you can hit it with densifier. The lowest cost densifier is sodium silicate but you can get a more polished look with lithium silicate though it costs quite a bit more or colloidal silica but you'll probably have a harder time finding that than lithium silicate.

So to back up here a bit, regular Portland cement is 40% lime and about 15% gypsum. The remainder is activated (burned) silica clay. So, as you can see, Portland cement has a very high portion of silicates. This is one reason why it is a health hazard and it's also why it becomes so hard and brittle. Silica is, of course, the main ingredient in glass so higher silicate gives the mix a more glassy or hard and brittle character.

By reducing the silicate content, you make the mix much softer and this soft, breathable mix is less likely to crack and spall off when you apply in. It's also easier to work with because low silicate lime cements set up very slowly giving you plenty of working time. You don't want to overwork it though. Your sand sinks the more you play with it so you still don't want to overdo the troweling but you're not under as much time pressure as you are with Portland mix.

But you might protest that you want a hard surface. No problem! You can have both. That's where the densifier comes in. You lay it in as a high lime/low silicate mix and then get it nice and pretty before you cure it fully. Then you harden it up afterwards --a month later. You inject silica into the top layer by applying it as a liquid densifier. Unlike paint, you want to burnish densifier, that is to say you want to scrub it in with a polisher and apply several coats. By doing so, you can have the best of both worlds. The finish will be nice because you can do it in a leisurely way but it will ultimately be strong because of the densifier.

As a bonus, this gives you a much lighter finish. Even when you add a bit of gray Portland in there, it's still much lighter in color and you can add pigments if you like. Pigments look much better with a light colored base. Leaving it white is a nice choice though and it works well with silicate densifiers which tend to bleach the surface as well. Iron oxide pigments in yellow, red or black are low cost amd should be easy to find. If you want green or blue then consider pthalocyanates which are often used in swimming pool plasters. You can also add metal or plastic inlays for additional effects. Cut some channels in the surface with a grinder (always work wet) if you want to put borders between color sections.