I found about 50 different sources for your quote, all verbatim copies of each other and without any indication of which those tablets were, who discovered them or any hint to catalogue numbers. I truly hate the internet sometimes, please treat this answer as a guess, there's no way to verify exactly which tablets the quote is about.
One of the tablets is (most probably) Plimpton 322 that lists Pythagorean triples and is part of the Plimpton Collection at Columbia University:
Plimpton 322 was indeed found in Senkereh, a site near the ancient city of Larsa, that's also known as Tell es-Senkereh, Tell as-Senkereh, Tell Senkereh, Sankarah, and Senkerah. Wikipedia says it was written about 1800 BC, the Rare Book and Manuscript Library of Columbia University is a lot less specific, dating the tablet between 1900 and 1600 BC, and Sherlock Holmes in Babylon asserts that the tablet's style suggests a 1600 BC origin (page 340), so the 2000 BC figure doesn't quite fit.
The 1854 figure is also bit problematic, but it roughly coincides with William Loftus' excavations in the area. Loftus discovered a few tablets, but his work in the area was rushed and under-documented, and as Edgar Banks (who later sold the tablet to George Arthur Plimpton) noted the findings were looted by locals. Without a solid record and with the tablets changing hands, I'm afraid a conclusive answer would be extremely difficult.
Another candidate would be AO 8865, a six sided prism with tables of squares, inverse squares and inverse cubes:
It has a similarly uncertain history with Plimpton 322 and it's dated at around 1750 BC.