Looks like the brain will burn 110cal/pound/day. So an average brain weight of 3lbs means 330cal/day total.
Hard for me to believe this number can increase to 10x that amount if we're to believe chess grandmasters are burning 6000cal/day (let's say 2300cal for the rest of the body, thus 3700cal for the brain). 6000 calories being the figure thrown around if you google it.
Sounds a bit like bullshit to me that a chess player can burn as many calories as a professional cyclist on an all-day race.