A radish line designated E66V70336 is disclosed. The invention relates to the seeds of radish cultivar E66V70336, to the plants and plant parts of radish cultivar E66V70336 and to methods for producing a radish plant, either inbred or hybrid, by crossing the radish cultivar E66V70336 with itself or another radish line. The invention further relates to methods for producing a radish plant containing in its genetic material one or more transgenes and to the transgenic plants produced by that method and to methods for producing other radish lines derived from the radish cultivar E66V70336.