"Admit to doing something" or "Admit doing something"

Hi there teachers, 

Do we admit to doing something or do we admit doing something? 

Here are the example sentences: 

- After being interrogated in the police lock-up for hours, he finally admitted to killing his friend. 

- After being interrogated in the police lock-up for hours, he finally admitted killing his friend. 

Are both the sentences given above correct and idiomatic, please? And do they have the same meaning? 

Thank you.