Black cockatoo is general descriptive term for cockatoos that are mainly black and may include:
Palm cockatoo, Probosciger aterrimus, also called great black cockatoo
Species of the genus Calyptorhynchus:
Red-tailed black cockatoo, Calyptorhynchus (Calyptorhynchus) banksii, has several alternative common names including black cockatoo
Glossy black cockatoo, Calyptorhynchus (Calyptorhynchus) lathami
Yellow-tailed black cockatoo, Calyptorhynchus (Zanda) funereus
Short-billed black cockatoo, Calyptorhynchus (Zanda) latirostris
Long-billed black cockatoo, Calyptorhynchus (Zanda) baudinii