The teenage defendant, who cannot be named for legal reasons, is accused of murder for causing the infant to suffer fatal injuries including a skull fracture, broken leg and rib fractures in the "deliberate" attack which happened in the early hours of February 11.
The baby's mother, aged 18 at the time, is on trial for child cruelty for failing to protect her baby or seek help for him.
Adam Feest QC, prosecuting at Winchester Crown Court, said the father, now aged 17, carried out the attack at the mother's one-room flat in Southampton, Hampshire, after the couple had spent the evening at a gathering at a neighbour's flat during which they were seen drinking vodka and beer.
Mr Feest said: "(The father) inflicted serious and fatal injuries to (the baby) who was just short of seven weeks old.
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"Most notable amongst those injuries was a serious complex skull fracture to the back of the head, a spiral fracture to the left femur, the long bone at the top of the leg, and numerous fractures to ribs, all of which were sustained very close to the time of his death.
"This taken together with other injuries, bruises, abrasions and significantly a bit to his nose show that he met with a violent end as a result of an assault or assaults perpetrated against him in a small flat where he was with his father and mother.
"Residents across the road recall hearing what they described as a blood-curdling or painful scream coming from the flat at about 3am."
He said one neighbour reported "a gut-wrenching cry of pain coming from a baby, a period of quiet then further screams of the same sort and the same direction".
"It was the sort of screaming that turned her stomach," Mr Feest added. "The crying continued as if nobody was attending the baby."
Mr Feest also said after the baby was rushed to hospital, the father told a neighbour: "What have I done?"
He added the bite mark on the baby's nose matched the father's dental prints.
Mr Feest continued: "The explanation he gave police was his son had accidentally fallen from the sofa when having his nappy changed or fallen from his arms when he and (the mother) were arguing.
"This cannot account for the severity and multiplicity of the injuries sustained. The injuries taken together are in keeping with a violent shaking or swinging, or indeed both."
Mr Feest said the mother, now aged 19, said she had not sought help because she did not want to lose her son or partner.
He said: "It may be she helped clear up the injury that (the father's) bite caused."
The jury was shown body-worn video footage of her crying in hospital saying the baby suffered the injuries in an accidental fall.
The defendants deny the charges and the trial continues.