In a known method for producing a porous carbon product, template material in the form of template particles, which contain macropores, and a polymerizable precursor substance for carbon are provided. The macropores of the template are infiltrated with the precursor substance in dissolved or melted form. After the carbonization of the infiltrated precursor substance, the template is removed in order to form the porous carbon product. According to the invention, in order to modify the method in such a way that a carbon structure having hierarchical porosity having a high fraction of mesopores having pore sizes in the range of 2 to 50 nm is obtained, after the infiltration according to step (c) and before the carbonization according to step (d), the precursor substance is subjected within the macropores of the template to a treatment at a foaming temperature at which the precursor substance foams under polycondensation and fills the macropores as substantially mesoporous foam, in which at least 70% of the pores have pore sizes in the range of 10 to 150 nm.