"And how much of that money is eaten up by the "services" that a16z provides..."

As a rule of thumbs, VCs take 2% of the fund's totally funding every year as "management fee", to pay for salaries, office rentals, marketing etc.

Therefore a16z's management fee from this specific fund is about $30M a year ($1.5B * 0.02).

However, please note that this is just the management fee of ONE fund. A VC firm often raises additional funds before a previous one ends its cycle (that's why you see fund names such as a16z fund I, a16z fund II, etc). a16z therefore has additional annual management fee from the previous, unfinished fund as well. I would not be surprised if a16z has $50M management fee per year across its multiple funds.

Source: I used to work for a VC.