Blastoise doesn't normally learn Blizzard nor Ice Beam, by leveling up. But if you teach it Bubble beam when it was still a Squirtle, it will learn the two said moves.
It seems that Bubble Beam also gets an upgrade from pokemon that evolves thus allowing you to learn those two other moves a pokemon wouldn't normally learn by simply leveling up.
With that said, is there any sites that shows a list of these moves upgrade from evolving pokemon?
EDIT: This was on the generation 1 (Pokemon yellow to be exact)