However, 8 USC 1325 doesn't actually use "illegal alien." Nevertheless, a search of the entire U.S Code at the Cornell University Law School's website yields 59 hits. So "illegal alien" is certainly there, copiously, within the Code.
Here's one example, with the disputed-by-the-ninnies phrase italicized throughout:
Title 8, Section 1365. Reimbursement of States for costs of incarcerating illegal aliens and certain Cuban nationals[I omit parts c, d, and e of 8 USC 1365.]
(a) Reimbursement of States Subject to the amounts provided in advance in appropriation Acts, the Attorney General shall reimburse a State for the costs incurred by the State for the imprisonment of any illegal alien or Cuban national who is convicted of a felony by such State. (b) Illegal aliens convicted of a felony An illegal alien referred to in subsection (a) of this section is any alien who is any alien convicted of a felony who is in the United States unlawfully andâ€” (1) whose most recent entry into the United States was without inspection, or (2) whose most recent admission to the United States was as a nonimmigrant andâ€” (A) whose period of authorized stay as a nonimmigrant expired, or (B) whose unlawful status was known to the Government, before the date of the commission of the crime for which the alien is convicted.