1. An image encoding device comprising: an image encoding unit configured to encode a plurality of sequentially input images to generate a plurality of encoded data that configures video data; and a code amount control unit configured to control a code amount of the encoded data generated in the image encoding unit such that the code amount of the plurality of encoded data in a cycle unit becomes a predetermined value, wherein the cycle unit is a cycle of periodic variation of the code amount of the encoded data or a cycle of periodic variation of complexity of the input images.