We propose the cube-based perceptual encryption (C-PE), which consists of cube scrambling, cube rotation, cube negative/positive transformation, and cube color component shuffling, and describe its application to the encryption-then-compression (ETC) system of Motion JPEG (MJPEG). Especially, cube rotation replaces the blocks in the original frames with ones in not only the other frames but also the depth-wise cube sides (spatiotemporal sides) unlike conventional block-based perceptual encryption (B-PE). Since it makes intra-block observation more difficult and prevents unauthorized decryption from only a single frame, it is more robust than B-PE against attack methods without any decryption key. However, because the encrypted frames including the blocks from the spatiotemporal sides affect the MJPEG compression performance slightly, we also devise a version of C-PE with no spatiotemporal sides (NSS-C-PE) that hardly affects compression performance. C-PE makes the encrypted video sequence robust against the only single frame-based algorithmic brute force (ABF) attack with only 21 cubes. The experimental results show the compression efficiency and encryption robustness of the C-PE/NSS-C-PE-based ETC system. C-PE-based ETC system shows mixed results depending on videos, whereas NSS-C-PE-based ETC system shows that the BD-PSNR can be suppressed to about -0.03dB not depending on videos.