彼は私の倍食べた。

English Translation

He ate twice as much as I did.

If no numeral is needed before 倍 for it to mean “two times,” would 二倍 then mean “four times”?

@ericaw

No, 2倍 always means “two times”. You cannot interpret 2倍 as “four times”.
倍 without numeral is just a shortened form of 2倍. So, you can rephrase the original Japanese sentence with 彼は私の2倍食べた.