It seems both options are possible:
admit (to) doing something [accept truth]
Dana admitted feeling hurt by what I had said.
admit doing something [accept blame]
Greene admitted causing death by reckless driving.
admit to (doing) something [accept blame]
A quarter of all workers admit to taking time off when they are not ill.
After questioning, he admitted to the murder.
No organization has admitted responsibility for the bombing.
Longman - admit
Student or Learner