New Schiff base complexes [Cu2(HL1)(L1)(N3)3]·2H2O (1) and [Cu2L2(N3)2]·H2O (2) were synthesized. The crystal structures of 1 and 2 were determined by single-crystal X-ray diffraction analysis. The HL1 ligand results from the condensation of salicylaldehyde and 1-(2-aminoethyl)piperazine, while a new organic ligand, H2L2, was formed by the dimerization of HL1 via a coupling of two piperazine rings of HL1 on a carbon atom coming from DMF solvent. The dinuclear building units in 1 and 2 are linked into complex supramolecular networks through hydrogen and coordination bondings, resulting in 2D and 1D architectures, respectively. Single-point and broken-symmetry DFT calculations disclosed negligible singlet–triplet splittings within the dinuclear copper fragments in 1 and 2. Catalytic studies showed a remarkable activity of 1 and 2 towards cyclohexane oxidation with H2O2 in the presence of nitric acid and pyridine as promoters and under mild conditions (yield of products up to 21%). Coordination compound 1 also acts as an active catalyst in the intermolecular coupling of cyclohexane with benzamide using di-tert-butyl peroxide (tBuOOtBu) as a terminal oxidant. Conversion of benzamide at 55% was observed after 24 h reaction time. By-product patterns and plausible reaction mechanisms are discussed. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.