James Allan Frederick Hemana was found guilty by an Auckland High Court jury in December of murdering baby Cezar Taylor in 2010.
He had earlier pleaded guilty to failing to provide the necessaries of life.
During his trial, the court was told how Cezar's mother Victoria Taylor, at the age of 20, had three children. Cezar was her youngest.
She broke up with her children's father before meeting Hemana and renting a home in Mangere.
The Crown said Hemana violently shook Cezar on two occasions in July 2010 but it was the second occasion which led to the baby's fatal injuries.
Giving evidence at the trial, Ms Taylor said Hemana picked up the child by one leg.
"He lifted him up, shook him, dropped him, picked him up, shake, shake, shake and dropped him.''
On the third occasion, the baby's head hit a cabinet before hitting the bed.
She said Cezar had been an alert, talkative baby but his condition changed after the attacks.
"Come Tuesday, he wasn't moving much, just sitting around ... As the week went on, he couldn't look and couldn't see. He looked like a zombie.''
Ms Taylor said Hemana stopped her from taking Cezar to the hospital and she had to stay home and "watch my baby look dead for a week''.
Her brother, Russell, told the trial Hemana referred to the baby as "Zombie Boy'' in the last days of his life.
He said he also heard Hemana call Cezar "lazy, that he was always tired and flickered his eyes ... things like that.''
