Old cocoyam: Colocasia esculenta; taro.
New cocoyam: Xanthosoma, particularly Xanthosoma sagittifolium, or the edible root of that plant; malanga.
A plant (Colocasia esculenta, but often identified as Colocasia antiquorum, among numerous other synonyms), which is usually considered a variety of C. esculenta, with edible starchy tubers.
The tubers of this plant.