I was wondering how the future block hashes are generated. Is this fully random or could this be influenced by someone?

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It's the digest of the block. Therefore any transaction/action that makes it into the block affects the calculated hash. It is "random" in the sense that the transactions and actions applied to the block are "random" (which is not really true, they are just typically not predictable).

Therefore, if you are able to influence the data contained in a block so that it results in a certain hash, you are able to influence the hash. It's very unlikely that this happens and that the there's a predictable outcome early enough to cause harm but it's theoretically not impossible.

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