Honestly it’s really sad but there are quite a couple.

If you like prehistoric history unfortunately I’m going to break your heart by mentioning how the original fossils of a Spinosarus were destroyed in Berlin by Allied bombers. This was a big lost for paleontology as it had been the only one in the world. Thankfully recently they found more bones for this unique Dino.

One specific example I’ll give is the cultural icons of Okinawa. Okinawa had its own unique culture and history. Shuri castle had been a symbol of the ancient rulers and its the place where Commodore Perry negotiated with the Okinawans. But during the war Shuri was not only bombed probably a good 100 times by allied planes and warships, but the castle actually burnt down. The ruins were even ruined. It’s amazing that they rebuilt it in modern times because many thought it was gone for good. But besides that, Japanese forces carved out cave systems in tombs. Ancestor worship was a huge part of Okinawan culture and the carving out of these tombs combined with Japanese forces looting them was a major problem for the culture of the island. US forces obviously destroyed much of these tombs but the US forces even looted. One colonel for example had to be begged to give back some Okinawan trinkets he snagged from the island. By the end of the war it all seemed lost, half of the Okinawans were killed ( 150,000 out of 300,000 were killed, give or take ) almost every town on Okinawa was destroyed, shuri was gone and Okinawan culture lay seemingly lost. Thankfully though a restoration movement has been able to recover this lost but unique culture.

I can give another specific example that was destroyed on purpose by the Nazis: the archives of the medieval Kingdom of Sicily and Naples.

In September 1943 Italy had capitulated to the Allies. The Nazis were still present in Italy though, and Naples was still under attack, so the archives were moved to a small village about30 kilometres from the city. The Nazis discovered them anyway, and the archivist explained that they were cultural heritage, important to both Italians and Germans, as well as all other Europeans. At first the Nazis left them alone, since they had no military value.

But on September 30, the local Nazi commander showed up and ordered everything to be burned. Why? No reason, apparently...just to punish the Italians for their defeat. There were tens of thousands of documents in hundreds of boxes and the vast majority of them were destroyed.

This is still a huge loss for medieval historians, even today. A lot of the documents had already been edited and published, which is helpful. But we always like to have access to the originals, and in this case, it's impossible now.

You can read more about this in an article by Laura K. Morreale at the Ultimate History Project, which has some further links and sources.