  Cubic transmuted (CT) distributions were introduced recently by
\cite{granzotto2017cubic}. In this article, we derive Shannon entropy, Gini's
mean difference and Fisher information (matrix) for CT distributions and
establish some of their theoretical properties. In addition, we propose cubic
transmuted Shannon entropy and cubic transmuted Gini's mean difference. The CT
Shannon entropy is expressed in terms of Kullback-Leibler divergences, while
the CT Gini's mean difference is shown to be connected with energy distances.
We show that the Kullback-Leibler and Chi-square divergences are free of the
underlying parent distribution. Finally, we carry out some simulation studies
for the proposed information measures from an inferential viewpoint.
