Is the Brain of Cthulhu a hard mode boss?
Solution 1:
No, Brain of Cuthulu is not in hard mode. Typically he is the second boss that you fight.
You will trigger hard mode once you defeat the Wall of Flesh.
Solution 2:
No he is not, It is a boss in easy mode. The hard mode bosses are very hard. You must defeat the wall of flesh to unlock the hard mode bosses, these are: The Twins, The Destroyer, Skeletron Prime, Plantera or Golem.