"You knew that you were likely to cause his death by doing what you did. You then delayed getting him to medical practitioners and then, to make matters worse, you lied about what happened."
Family members, including Popo's mother, carried pictures of the baby and wept after the sentencing.
A spokeswoman for the family, Moeroa Asiata, read a statement on their behalf outside of court.
"While the sentence does not bring any sense of relief or peace for our family, it does give us a sense that justice has been served," the statement said.
The family thanked the Crown, police and their extended family for their support.
The court was told that Popo and his parents had been living next door to Filihia and her family during 2011.
The families became close friends and Filihia sometimes looked after Popo.
On November 4, 2011, as she was giving Popo a bath, she became angry with the helpless baby and struck his head against a flat surface with "significant brutality", the Crown said.
Filihia initially told doctors that nothing unusual had happened but later changed her story and said he had fallen from a deck.
Justice Gilbert said there were no mitigating features which could lessen the sentence he handed out.
The offending was aggravated by Popo's vulnerability and the fact Filihia had been in a position of trust, he said.
Popo was taken to Starship Children's Hospital where an MRI found a skull fracture in the back of his head. He had bleeds on the surface of his brain and extensive brain damage.
He died two days later.
Justice Gilbert accepted that Filihia's actions were not pre-meditated and she had not intended to kill the baby.
She continues to deny that she was responsible for his death.
Speaking outside court, her lawyer Mark Edgar said she was considering an appeal.
"In her eyes, she continues to deny responsibility."
Filihia has three children, and Mr Edgar said her family was "absolutely shattered" by what happened.
