There are disclosed a method for preparation of the solid oxide fuel cell single cell and a single cell with nano (micro) meso porous cathode electrode that are operational from 723 to 1073 K. The cathode electrode of the single cell possesses very large surface area (10-500 m2 g−1) with the hierarchical nano (micro) mesoporous structure, very high catalytic activity and very low oxygen electroreduction activation energy varying from 0.3-0.8 eV at −0.2 . . . 0 V cathode electrode potential versus porous Pt/O2 reference electrode in air.