We present our recent results on the growth of cubic AlN (001) layers by plasma assisted molecular beam epitaxy (PAMBE) using freestanding 3C-SiC (001) substrate. For high-quality c-AlN layers reflection high-electron energy diffraction (RHEED) patterns in all azimuths show RHEED patterns of the cubic lattice, hexagonal reflections are absent. High-resolution X-ray diffraction (HRXRD) measurements confirm the cubic structure of the c-AlN layers with a lattice parameter of 4.373 Å. Atomic force microscopy (AFM) scans show an atomically smooth surface with a roughness of 0.2 nm RMS. Ellipsometry studies yield the dielectric function (DF) of c-AlN from 1 to 10 eV. The direct gap is determined with 5.93 eV at room temperature, while the indirect one is below 5.3 eV (onset of adsorption). The high-energy part of the DF is dominated by two transitions at 7.20 and 7.95 eV attributed to critical points of the band structure.