The concept of cubic m-polar fuzzy set (CmPFS) is a new approach to fuzzy modeling with multiple membership grades in terms of fuzzy intervals as well as multiple fuzzy numbers. We define some fundamental properties and operations of CmPFSs. We define the topological structure of CmPFSs and the idea of cubic m-polar fuzzy topology (CmPF topology) with P-order (R-order). We extend several concepts of crisp topology to CmPF topology, such as open sets, closed sets, subspaces and dense sets, as well as the interior, exterior, frontier, neighborhood, and basis of CmPF topology with P-order (R-order). A CmPF topology is a robust approach for modeling big data, data analysis, diagnosis, etc. An extension of the VIKOR method for multi-criteria group decision making with CmPF topology is designed. An application of the proposed method is presented for chronic kidney disease diagnosis and a comparative analysis of the proposed approach and existing approaches is also given.