Like many early filmed television program, not much information is available about The Cases of Eddie Drake, either online or in the standard print television encyclopedias. A single episode is available on DVD as part of the Best of TV Detectives (150 Episodes) from Mill Creek Entertainment. That same episode is also available online at the Internet Archive. Most people, were they to watch the episode, would likely never give it a second thought. But not Michael Shonk, who has written a three-part history of the series for the Mystery*File blog: Part One, Part Two, Part Three.
Shonk addresses several mysteries, including how many episodes were produced, when they were originally aired and how CBS, NBC and DuMont were (or weren't) involved. His investigation is thorough and intriguing.
Most sources point to thirteen episodes having been filmed, the first nine in 1948 and an additional four at some point perhaps years later. That is where much of the confusion lies. Also in question is what the DuMont network had to do with the series. Most sources state that DuMont aired The Cases of Eddie Drake between March and May of 1952. My belief is that the series had nothing to do with DuMont (it aired locally in New York City over WABD-TV in 1952) and was syndicated beginning in mid-1951.
The Paley Center for Media has ten episodes of The Cases of Eddie Drake in its collection, which is pretty good all things considered. I cannot find any record of the series at UCLA's Film and Television Archive or the Library of Congress. And the Museum of Broadcast Communication's archives are currently offline and not searchable.