You are correct, that some do pay taxes. It is estimated that Illegal aliens pay about $11.6 billion in taxes per year.
However, it is also estimated that illegal aliens cost the U.S. taxpayer about $100 - $195 billion per year. So what they pay in taxes is a small percentage of what they cost the economy.
As far as benefits, if they go to an ER and can't pay, we pick up the cost. In addition, their children get to attend school for free and they receive free meals, etc. If any of their children are born here, they are also eligible for Medicaid, foods stamps, etc.
Additionally, the cost to apprehend, process, track, deport, and adjudicate all the legal issues with being an illegal alien is also expensive.
Illegal aliens are not a net gain to our economy.