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Based on Cynk-Hulek method we construct complex Calabi-Yau varieties ofarbitrary dimensions using elliptic curves with automorphism of order 6. Alsowe give formulas for Hodge numbers of varieties obtained from thatconstruction. We shall generalize result of Katsura and Sch\"utt to obtainarbitrarily dimensional Calabi-Yau manifolds which are Zariski in anycharacteristic $p\not\equiv 1\pmod{12}.$

Higher dimensional Calabi-Yau manifolds of Kummer type