Multi-parametric MR images have been shown to be effective in the non-invasive diagnosis of prostate cancer. Automated segmentation of the prostate eliminates the need for manual annotation by a radiologist which is time consuming. This improves efficiency in the extraction of imaging features for the characterization of prostate tissues. In this work, we propose a fully automated cascaded deep learning architecture with residual blocks, Cascaded MRes-UNET, for segmentation of the prostate gland and the peripheral zone in one pass through the network. The network yields high Dice scores ($0.91\pm.02$), precision ($0.91\pm.04$), and recall scores ($0.92\pm.03$) in prostate segmentation compared to manual annotations by an experienced radiologist. The average difference in total prostate volume estimation is less than 5%.