Two new coordination compounds with tetracopper(II) cores, namely, a 1D coordination polymer, [Cu4(μ4-H2edte)(μ5-H2edte)(sal)2]n·10nH2O (1), and a discrete 0D tetramer, [Cu4(μ4-Hedte)2(Hpmal)2(H2O)]·7.5H2O (2), were easily self-assembled from aqueous solutions of copper(II) nitrate, N,N,N',N'-tetrakis(2-hydroxyethyl)ethylenediamine (H4edte), salicylic acid (H2sal), or phenylmalonic acid (H2pma). The obtained compounds were characterized by IR and electron paramagnetic resonance spectroscopy, thermogravimetric and elemental analysis, and single-crystal X-ray diffraction. In addition to different dimensionalities, their structures reveal distinct single-open [Cu4(μ2-O)(μ3-O)3] (in 1) or double-open [Cu4(μ2-O)2(μ3-O)2] (in 2) cubane cores with 3M4-1 topology. In crystal structures, numerous crystallization water molecules are arranged into the intricate infinite 1D {(H2O)18}n water tapes (in 1) or discrete (H2O)9 clusters (in 2) that participate in multiple hydrogen-bonding interactions with the metal-organic hosts, thus extending the overall structures into very complex 3D supramolecular networks. After simplification, their topological analysis revealed the binodal 6,10- or 6,8-connected underlying 3D nets with unique or rare 6,8T2 topology in 1 and 2, respectively. The magnetic properties of 1 and 2 were investigated in the 1.8-300 K temperature range, indicating overall antiferromagnetic interactions between the adjacent Cu(II) ions within the [Cu4O4] cores. The obtained compounds also act as bioinspired precatalysts for mild homogeneous oxidation, by aqueous hydrogen peroxide at 50 °C in an acidic MeCN/H2O medium, of various cyclic and linear C5-C8 alkanes to the corresponding alcohols and ketones. Overall product yields of up to 21% (based on alkane) were achieved, and the effects of various reaction parameters were studied.