Is there Blocks pruning in ethereum clients such as geth and how does that work? by pruning I meant, does the blocks information whether stored in DB like in cpp-ethereum are deleted if the blockheight is beyond a certain block height range? This question is related to saving storage space.
If so, how does it happen? does it just straightforward delete the blocks beyond the range or is there any other computation going on there to make sure the integrity of the chain?
Blocks aren't pruned. They are stored in geth/chaindata/ancient directory and you can't delete them because your Geth is serving this information to other nodes that at any point in time would need to sync just like you.
The only pruning that takes places is State pruning, old state objects are deleted from Merkle Trie as new blocks are added.
The latest addition in space saving implemented in geth was transaction unindexing, as a part of 1.10 version. Now old transactions are deleted saving about 40GB of space. This is the default.
So, if any option to save disk would exist, it would be implemented, but currently the space is as optimal as it can be.
There is another project that has a goal of optimizing resources called Erigon, so you might to check it
