"I admit having" is correct and usable in written English.
It is used to express some form of ownership, usually with the understanding that the ownership may not be desirable or something to be proud of. For example, "I admit having made a mistake."
"I admit having taken large positions that could be qualified... as outside the limits of my mandate, and which I masked by a fictitious transaction.
At the September 13th bond hearing, held in Magistrate Judge Stickney's court the day after my arrest, Special Agent Allyn Lynd took the stand and claimed under oath that in reviewing my laptops he had found discussions in which I admit having engaged in, quote, "SWATting", unquote, which he referred to as, quote, "violent activity", unquote.
I admit, having in the past few days alone been called a "cock", an "idiot", "scum", a "wanker" (bless) and – worst of all – a "Republican" by commenters, I too am close to installing the TC comment blocker Chrome extension.
I admit having fewer experiences than stereotypes of "Mormons" -- including "conformist" and "closed-minded".
I'm 28, single, and obsessed with my job, so I admit having babies is low on my list of priorities.
My experience, I admit, had some effect on the questions I later asked project makers.
This strategy has, I admit, had something of a patchy hit-rate.
I have to admit, having been a lawyer, I'm a big Judge Judy fan.
The next challenge was bacalhau, an ingredient that, I must admit, has never really wowed me.
This diplomatic effort, the government of Israel — with some misgivings, I readily admit — has generally supported.
The protection, I must admit, hasn't worked very well this year.
