What is the most expensive part of mining?

What is the most expensive part of mining?

From my understanding, miner's take a bunch of transactions and use a nonce, previous block and the transaction data to try and find a hash that beats the difficulty. As soon as this happens, will their block be added, and then 99 blocks later the BTC will be awarded.

Is the solving aspect of the hash the most expensive part, for the computer? Or is gathering the transactions and confirming them more expensive?

How does one confirm the transactions? Do they have to traverse the entire blockchain, or only find the most recent ledger which shows both user's balances to confirm?

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