I was initially going to suggest using a Patio cleaner, which we applied to the concrete paving slabs in our patio with a stiff brush which cleaned it up beautifully.. However, I'm not sure whether this would damage the black marble content . However, you could experiment with a tiny patch and see if it works. Otherwise I think you'd be save using hot soapy water. If you want to try and restore the "lustre", there's a patio sealant which can be brushed onto concrete slabs to seal it after it has been jet washed, which is a punishing process and takes away the protective surface. It leaves it with a very slight sheen, rather than a glossy surface.