Nucular is an ad hoc spelling

Eye dialect

Eye dialect is the use of non-standard spelling for speech to draw attention to pronunciation. The term was originally coined by George P. Krapp to refer to the literary technique of using non-standard spelling that implies a pronunciation of the given word that is actually standard, such as...

 of a metathetic

Metathesis (linguistics)

Metathesis is the re-arranging of sounds or syllables in a word, or of words in a sentence. Most commonly it refers to the switching of two or more contiguous sounds, known as adjacent metathesis or local metathesis:...

 mispronunciation of the word nuclear

Atomic nucleus

The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...

, representing the pronunciation ˈnjuːkjələr (Canada) or ˈnuːkjələr (United States) of that word instead of the standard pronunciation, /ˈn(j)uːkliːər/.

While most dictionaries do not list the pronunciation as correct, some recognize it because of its increased usage.
In addition to the above-discussed role of the "word" as a mispronunciation, there is also a pre-existing though rarely used word in botany, "nucular" which is defined as "of or related to a nucule", which is a section of a compound (usually hard) fruit.

Merriam-Webster Dictionary

Merriam-Webster

Merriam–Webster, which was originally the G. & C. Merriam Company of Springfield, Massachusetts, is an American company that publishes reference books, especially dictionaries that are descendants of Noah Webster’s An American Dictionary of the English Language .Merriam-Webster Inc. has been a...

:

"Though disapproved of by many, pronunciations ending in \-kyə-lər\ have been found in widespread use among educated speakers, including scientists, lawyers, professors, congressmen, United States cabinet members, and at least two United States presidents and one vice president.