A 23, 24, and 26-year-old are due to reappear in court this month, and another 26-year-old will reappear in January.
Adkin says inquiries are ongoing and more charges are likely.
The attack was "an absolutely tragic event for the Fuatimu family," he said.
"They are completely devastated to lose a much-loved son and brother," Adkin said.
Fuatimu and his friends were at a property playing music before they moved to the park.
Adkin says two men started an attack against a group socialising at the park.
They fled afterwards. Police were working through CCTV footage to establish the identity of the offenders, whom Adkin described as Pacific Islanders.
There was no information to suggest they were known to the victims.
Items of interest were removed from the park, but police did not specifically address whether a weapon was involved in the attack.
"We want those people who were at the park to come forward or anyone who knows the offenders," Adkin said last week.
He urged those responsible to do the right thing for Fuatimu and his family.
"We believe there are people within the community who know exactly what happened and know the identity of those involved."