Three new tetracopper(II) coordination compounds were easily generated from Cu(NO3)2, a trifunctional aminoalcohol sulfonic acid (H3bes, N,N-bis(2-hydroxyethyl)-2-aminoethanesulfonic acid) as a principal building block, and a benzene carboxylic acid as a supporting ligand (i.e., benzoic (Hba), 4-hydroxybenzoic (Hfba), or 3-hydroxybenzoic (Hthba) acid). The obtained microcrystalline products, [Cu4(µ-Hbes)3(µ-H2bes)(µ-L)]·2H2O (L = ba− (1), fhba− (2), and thba− (3)), were fully characterized by FTIR (Fourier-transform infrared spectroscopy), elemental analysis, ESI-MS (Electrospray Ionisation Mass Spectrometry), and single-crystal X-ray diffraction methods. Compounds 1–3 were applied as effective homogeneous catalysts in the oxidative C−H functionalization of alkanes (cycloalkanes and propane). Two different model reactions were explored: (1) mild oxidation of alkanes with hydrogen peroxide to give alcohols and ketones, and (2) mild carboxylation of alkanes with carbon monoxide, water, and potassium peroxodisulfate to give carboxylic acids. For these reactions, effects of different parameters, as well as mechanistic and selectivity characteristics, were studied.