Convolutional neural networks (CNNs) require large amounts of data for training, beyond what can be acquired for current radiomics models. We hypothesize that deep entropy features (DEFs) derived from existing CNNs can be applied to MRI images of prostate cancers (PCa) to reliably predict the Gleason score (GS) of PCa lesions. In this study, we analyzed 112 lesions acquired from 99 PCa patients, either pre-biopsy or pre-treatment, their associated GS, and multi-parametric MRI (mpMRI) sequences. Our approach is based on the extraction of DEF features produced in individual layers of 9 pre-trained CNN models. We first analyze DEFs from separate CNNs using the Wilcoxon test and Spearman correlation to find significant features associated with GS. In a multivariate analysis, we then use the combined DEFs of all CNNs as input to a random forest (RF) classifier for predicting the Gleason grade group of patients. Among the 9 pre-trained CNNs, the NASNet-mobile architecture offered the features most correlated to GS ($\rho =0.47$ ; p