Connor's act of selflessness in trying to rescue Cubix from the crumbling building is what brought him to life again, just in time to save them both. It was never a matter of hardware but of heart, that fixed the 'Unfixable Robot'.
When the explosive Antix attach themselves to Cubix, he flies off faraway into the sky Iron Giant style to protect his friends from the explosion.
Professor Nemo's pep talk to Connor, explaining Cubix's true source of strength is not his Solex but the embodiment of faith that Connor has in him. With renowned strength, Connor is able to bring Cubix back to life once more.
Connor finding Cubix barely alive amongst the wreckage of the Kulminator, yet Cubix continues to remain positive even as he runs out of Solex.
When Cubix comes back to life after sacrificing himself to save the town from Dr. K's Humongous Mecha in the season one finale. Only someone with a hard heart couldn't get tears in the eyes seeing that.