All the graphs considered in this paper are simple and undirected. Let [Formula: see text] be a simple undirected graph. A function [Formula: see text] is called root cube mean cordial labeling if the induced function [Formula: see text] defined by [Formula: see text] satisfies the condition [Formula: see text] and [Formula: see text] for any [Formula: see text], where [Formula: see text] and [Formula: see text] denotes the number of vertices and number of edges with label [Formula: see text], respectively, and [Formula: see text] denotes the greatest integer less than or equals to [Formula: see text]. The [Formula: see text] is called root cube mean cordial if it admits root cube mean cordial labeling. In this paper, we have discussed root cube mean cordial labeling of some graphs. Also, we have provided some graphs which are not root cube mean cordial.