The noun cadre (describing a small group of people, often united by a political purpose) comes directly from the French word cadre, which meant "framework". The meaning had shifted to "organizational framework", particularly for military groups, and eventually came to be applied to all sorts organized groups, from communists to scientists. The French word was also not pronounced with the e at the end, but Americans started saying it because they assumed that the word came directly from Italian or Spanish, where the final vowels are pronounced. Going back further, it does in fact derive from Italian quadro, meaning "square" (the connection was the idea of a military formation). That's from Latin quadrum, which is related to quattuor, the word for "four". Finally, it all derives from the Proto-Indo-European reconstruction kweter, meaning "four" (also the source of everything from quarrel to squad and farthing).
Hello! I'm Adam Aleksic. This year, I graduated from Harvard University with a degree in Government and Linguistics. There, I co-founded the Harvard Undergraduate Linguistics Society and wrote a thesis on Serbo-Croatian language policy, magna cum laude. In addition to etymology, I also really enjoy philosophy, trivia, vexillology, geography, board games, conlanging, art history, and law.