Exploring the topological structures of networks by mathematical methods is powerful and efficient in researching real networks. There are many successful mathematical methods shown in scale-free networks that are forming branches of mathematics and network science. We are motivated from the cumulative degree distribution and edge-cumulative degree distribution of scale-free networks, and discover several newly mixed cumulative distributions for scale-free networks. By three classical scale-free networks we compute our mixed cumulative distributions, we, also, discover some phenomenons between known and new cumulative distributions. Some problems are presented for further investigate scale-free networks.