The 23-year-old inflicted catastrophic head injuries on seven-week-old Lucas at Benalla in northeast Victoria in October 2019. The infant died five days later in hospital.

Doctors told Lucas's distraught mother, Samantha Duckmanton, and McDonald, that the baby died from "non-accidental injuries" including swelling around the brain.

McDonald has since admitted killing Lucas and details of the case were the basis for a hearing in Victoria's Supreme Court on Friday.

Shortly after Lucas's death, Ms Duckmanton confronted McDonald, demanding he explain what happened to their child.

The killer then hid in a horse shed on a paddock nearby the hospital, where he slept for two days before being found by a local resident.

McDonald gave the man a false name and story about being robbed, bashed and taken from his vehicle.

He subsequently spent a night in and around the small town of Wallan, about an hour north of Melbourne, before handing himself in to police, who charged him with murder.

McDonald, who has served 399 days in custody, pleaded guilty in Victoria's Supreme Court on Friday to child homicide.

Prosecutor Mark Gibson SC said the former saw mill worker had anger management and conflict resolution problems, and had shown only a "degree of remorse".

Ms Duckmanton told the court Lucas's death was the worst day of her life.

"All the things you took can never be replaced," she wrote in a statement to the court.

"I'll forever feel guilty for not protecting Lucas because I trusted you.

"I had such plans, hopes and dreams for my boy.

"You do not deserve forgiveness or the title of 'Daddy'."

The court also heard McDonald was addicted to PlayStation and was playing games on the console after inflicting what would be the fatal head trauma upon his son.

Ms Duckmanton heard a "high-pitched cry" from Lucas at the time.

McDonald's lawyer, Colin Mandy SC, told the court his client was "profoundly sad, regretful and remorseful".

"The breaking of all those hearts - Mr McDonald knows and accepts he is responsible for that," Mr Mandy said.

"He will carry that burden."

Justice Stephen Kaye said the 23-year-old's offence would be "more serious" if he was older and had more life experience.

"He is a young man, very immature, in a situation with two very young children and he simply wasn't coping," Justice Kaye said.

"But he has to learn there is a price to pay when he can't control his violence."

McDonald is due to be sentenced later in December.

Australian Associated Press