This is my theory about Nuka and his life.
Before I start, I just want to say I've already read some theories about Zira's cubs, most of which I can agree with. Enjoy!
What We Know
In SP, Nuka is a termite-infested lion who lives in the Outlands. He considers Zira as his mother, Vitani as his younger sister, and Kovu as his younger brother. He despises Kovu for being "hand-picked" by Scar to be the heir of Pride Rock. As resentful he is, he tries to please his mother. This results in his death.
As in the musical, Scar is desperate for a queen. He finds Zira to be a suitable mate. She was determined, loyal, and shared his political views. Zira births Nuka towards the later half of Scar's rule. Other males born were killed off so they wouldn't grow to challenge him. Scar and Zira consider Nuka to be the heir, but they think he is too young to be told he is the heir.
Scar was looking for an heir that would have a presence of power, austurity and cunning. An heir that would learn his political views and carry them out exactly as he would. Someone younger, but had the wisdom of an elder. As the days went by, Nuka, unfortunatly was failing to meet his father's requirements.
Seeing that Nuka was getting worse every day, Scar was in heavy need of a new heir. Towards the final months of his rule, a lioness, (I personally have no theory of who Vitani's mother was) gave birth to Vitani. Scar did sire her, but he had no desire for a female to be his heir. Later, Kovu was discovered. (Once again, no theory about Kovu)
Seeing that Kovu was his best chance, Scar began to train him. Zira was disappointed with her son, and she gave her attention to assist with the training of Kovu. Even though Vitani was rejected, Zira considered her to be helpful to her. She trained Kovu and Vitani together, forgetting about her own son, Nuka. Nuka was ignored by both Scar and Zira, so he developed a cold attitude towards his father.
Scar was killed, and all lions/lionesses that were loyal to him posed as a threat to Simba. Simba banished them all to the Outlands. The original mother of Vitani no longer wanted her cub anymore, so she let Zira take her away.
Over time, Nuka still craves attention from his mother, who still focuses on Kovu. Naturally, he becomes jealous and bitter. Eventually, Nuka figures out that being the first born to Scar, he should have been the heir. Nuka grows more bitter towards his younger "brother" and father (he no longer considers him to be a father, just "Scar"). Nuka learns to take care of himself, only to get his pelt infested with termites.
As an adult, he resembles his father, but his issues worsen. Nuka is unable to leave his father's pride because he's waiting for the right chance to overpower his brother, get the attention of Zira, and take his place as king. He sees this opertunity when Kovu failed Zira and Simba is struggling for his life. Nuka recklessly climbs up the log dam, while doing so he's pleading for Zira to watch him.
"I'm doing it for you, and I'm doing it for me!"
Nuka despised Scar so much, that he has become him. He's proving it more to himself than his mother that he is capable of becoming more than he is considered. Nuka manages to snag Simba's ankle, but a log slips, and Nuka falls and is crushed.
During his final moments, he apologizes to his mother for being an unsatisfactory son.
"I'm sorry, Mother. I tried.... Didn't I...?"
Hope you enjoyed it! -Beautiful Stranger