After beating the Pokemon League, you still can't go to the Cerulean Cave. To be able to enter you have to get the National Dex by catching 60 different types of Pokemon and showing your PokeDex to Professor Oak, also you have to do the Ruby Sapphire side quest in the Sevii Islands. By then you will be able to enter the Cerulean Cave that contains Pokemon levels 50-60 and Mewtwo Level 70 at the Bottom floor of the Dungeon.
Maybe this videos will help:
http://www.YouTube.com/watch?v=2vOwD9JCnZg&feature=related
http://www.youtube.com/watch?v=c4guYVGMwgY&feature=related
http://www.youtube.com/watch?v=rIIfmODFQJo&feature=related
http://www.youtube.com/watch?v=YEjwjFv3ovA&feature=related
http://www.youtube.com/watch?v=lNMu4nwDVig&feature=related
http://www.youtube.com/watch?v=Q5ddprvQo5g&feature=related
http://www.youtube.com/watch?v=lZfl0XSzm9s&feature=related
http://www.youtube.com/watch?v=XOn1NHpxUIA&feature=related
These videos are the videos that show you how to get Mewtwo since you have the NationalDex And have beaten the elite 4 once.
Cerulean cave
lost cave
Yes it is in a cave.
In icefall cave.
in cerulein cave very back
You can find the Cerulean Cave in the northwest corner of Cerulean City in Kanto in Pokemon LeafGreen. The cave contains the Pokemon Mewtwo.
There is no awakening cave.
in cerulean cave.
Diglett cave
How to get to lost cave in leaf green??
Altering cave is on 5 or 6 island.
that would depend on which cave, for there are many caves in leafgreen.
There not in cerulean cave.
back of cerulean cave
on four island
its on 4 iland
lost cave