Probers must answer in detail how so many bureaucrats left Zymere at mercy of two brutes.

The brutal beating death of 6-year-old Zymere Perkins after a life of nightmarish cruelty demands the full weight of criminal justice for his killer or killers — and unsparing accountability for Mayor de Blasio. Zymere urgently needed protection from his mother and her body-building boyfriend — the image of whose powerful fists is impossible to bear.

Whatever role either played, or did not play, in the inhuman pummeling that made hell of Zymere’s last conscious moments, the couple had enablers in the city agencies who are charged with preventing such tragedies.

They cannot plead ignorance because they had numerous warning signs that, in the custody of unstable and irresponsible adults, Zymere was at high risk of peril.

Still more, de Blasio cannot get by with the balm of public heartbreak and talk about “systems” that failed and that must be reformed. Nor should the public vest any faith in the announcement of a probe by the Department of Investigation.

Headed by former de Blasio campaign treasurer Mark Peters, DOI has an unbroken record of issuing reports that avoid naming whom among the mayor’s inner circle has done anything wrong.

There is scant likelihood that Peters would highlight how mayoral policies, budgeting and oversight contributed to breakdowns by the Administration for Children’s Services, Department of Homeless Services and Department of Education, among others.

With de Blasio bearing ultimate responsibility for the collective failures on his watch, New Yorkers — and more important Zymere — deserve a comprehensive, independent review of who and what went wrong, and why. Only Gov. Cuomo has the power to order such an investigation — if need be through the use of a special non-prosecutorial grand jury.

Investigators must publicly answer in specific detail how so many city bureaucrats paid to protect children left Zymere at the mercy of brutes Geraldine Perkins and Rysheim Smith.

All told, Perkins was the subject of five reports to ACS of maltreatment dating back to the child’s infancy in 2010. Appallingly, the agency received four of the reports in the last two years. They included a call to police by a school social worker who saw bruises on Zymere’s legs.

But, each time, child protective investigators cleared Perkins under circumstances covered by confidentiality laws. How could they?

Zymere and his family lived in homeless shelters in Queens and Harlem, where neighbors say they witnessed unmistakable evidence of abuse, and one says that Zymere’s tormentors beat her when she tried to intervene.

Did Department of Homeless Services staff fail to see or hear, or did they stay mum about what they saw and heard?

This year, Zymere was not enrolled at school at all. Did anyone at either ACS or the Department of Education know or act? Did child welfare investigators even visit the home to learn what might be amiss?

If anyone had, they might have learned from neighbors that Zymere was rarely seen emerging from an apartment that relied for electricity on an extension cord run into the hallway.

How many times have investigators visited in all, and what did they and didn’t they ask or see?

Zymere plummeted through gaping holes in the child protection net that de Blasio had committed to close, following the fatal torture of 4-year-old Myls Dobson at the start of 2014. Then, ACS admitted that it had failed to investigate allegations of domestic violence or to seek emergency foster care and had no clue the boy’s dad, supposedly caring for him, was incarcerated — even as caseworkers visited the child nine times.

“The agency’s duties and our duties are to make sure that something like this doesn’t happen again,” the mayor vowed.

De Blasio’s hasty solution to profound failures of communication between government agencies was to establish a Children’s Cabinet headed by Deputy Mayor Richard Buery to “develop strategies for a holistic approach to a child’s safety and well-being,” in the words of a press release.

“Holistic” anything has no place in the hell from which Zymere needed to escape. Why was he not placed in the safer haven of foster care?

Tragically, Zymere was not alone in his abandonment by city authorities. In May, DOI documented appalling, fatal mismanagement of child welfare investigations, including absentee casework and failure to report abuse.

But, in keeping with Peters’ practice of shielding higher-ups, his report named not a single ACS official, not even Commissioner Gladys Carrion, as responsible.

Little wonder that avoidable fatalities continue to happen under the watch of an agency and a mayor without a true watchdog.

A fresh outside investigation — naming names, detailing every move — must lead to a new era of accountability within ACS and with the public that entrusts the agency to protect New York City’s youngest.

A fervent believer in the benefits of keeping troubled families together and children out of a rapidly shrinking foster care system, de Blasio gets no more chances to test his starry-eyed notions on the lives of defenseless kids.