You can refinish cultured marble however you cannot change the pattern or color. This is because the marble dust and epoxy are mixed together and pour into a mold.
To refinish cultured marble you will need to sand it down to remove all the scratches. Start with the highest grit sandpaper that will do this. Then repeat the process until your cabinet has a nice satin finish. The sandpaper grits should be about what I have written below.
80 grit 150 grit 250 grit 350 grit 400 grit
Clean your countertop with a paint thinner to remove all the dust.
Now you must place a clear coat over your countertop. I use a special two part clear epoxy designed for this purpose, however it is quite expensive and requires some experience. A clear exterior grade polyurethane might work. You might need to apply 2-3 coats.