You must beat the Elite Four before you are allowed access to it.
if can go to cerulean cave you can
you get mewtwo in the cave next to cerulean c:
I know that on pokemon blue there is a mewtwo in the cave at cerulean, as for leaf green or fire red I don't know but I would guess that there is a mew or some other sort of rare pokemon inside
There not in cerulean cave.
You can get all the Pokemon in the cerulean cave where you find celebi below the cerulean cave.
In Pokémon HeartGold, you can gain entry into Cerulean Cave once you've defeated Blue.
You can find the Cerulean Cave in the northwest corner of Cerulean City in Kanto in Pokemon LeafGreen. The cave contains the Pokemon Mewtwo.
You can capture one in cerulean cave or train a magnemite to level 25.
Cerulean Cave can only be found in the first-gen games, such as Red, Blue, Yellow, Fire-Red and Leaf-Green. Hope this helps! :D
Mewtwo
MEWTWO
Unknown Dungeon was the name of a cave in Red, Blue and Yellow version that is located northwest of Cerulean City you would need Surf to reach their the cave is now called Cerulean Cave.