BOTH pronunciations are correct.
nu·cle·ar (nōō'klē-ər, nyōō'-)
Usage Note: The pronunciation (nōō'kyə-lər), which is generally considered incorrect, is an example of how a familiar phonological pattern can influence an unfamiliar one. The usual pronunciation of the final two syllables of this word is (-klē-ər), but this sequence of sounds is rare in English. Much more common is the similar sequence (-kyə-lər), which occurs in words like particular, circular, spectacular, and in many scientific words like molecular, ocular, and vascular.
No wonder the PaulBots bash Sarah Palin on FR.
Sarah is the one speaking out for the defense of
our Nation.
The PaulBots would rather have a candidate hand out shovels
to dig holes to bury our heads.
Noo-kyu-ler has become an accepted, albeit substandard, alternative just as the equally cringe inducing Illinoiz has for Illinois.
nuclear= nuke-u-lar (or if you are a nit-picker it can be pronounced nuke-lee-ar)