Do cocketiels and parakeets get along?
There have been cases where they do, but it is not recommended to mix different species of birds in the same cage. Cockatiels are much bigger than parakeets, and can cause serious damage from a single bite.
In short, yes. The key is can those two specific blue parakeets get along. Color doesn't matter, but the two parakeets personalities may clash. If you have had a parakeet for a long time, he may not take kindly to an intruder. Often if you have three, two will bond and pick on the outsider. It is really about the individual birds not the color.
Cockatiels and budgies can get along perfectly together if given enough space. You need to make sure their cage is big enough or else they may fight which is bad news for the budgie! Cockatiels are very docile and sedate, Budgies are quite aggressive , and will terrorize Cockatiels, it has nothing to do with size, they should have separate cages, no parrot species should ever be mixed.