I too wouldn't mind knowing this, I thought about it when I spotted this
Block for sale in the Collectibles section.
That "block" is the physical representation of the private key containing the miner's reward plus fees for Block number mentioned. Those physical collectibles have their private keys laser-etched and with a hologram covering it. So if you peel it off, this reveals the private key which you can use to claim the "virgin" BTC which was mined in that old block.
This also means that it'll have a bunch of forked coins including 25 BCH, 25 BTG etc etc.
If i understand correctly, OPs question is whether the bitcoin blocks that are viewable on blockchain explorers contain the private key (in some form). The answer is clearly No. Also, Blocks don't have private keys. They have block headers and the all the transaction IDs.
I too wouldn't mind knowing this, I thought about it when I spotted this
Block for sale in the Collectibles section.
I know that private key to the genesis block can control the entire blockchain.
WTF are you talking about? Nothing can control the ENTIRE blockchain my friend? Not the genesis block, not even Satoshi's private keys.