The seven-goal winning margin matches is Chelsea's biggest Youth Cup win in history, while it is the first time they have scored eight or more in the competition since 1997 – one better than the seven they managed against Wolves last season.
"It's an amazing feeling to captain Chelsea in the Youth Cup this year. I had the armband in the final earlier this month through Tino Anjorin's absence and it was an honour then," Bate told the official Chelsea website. "Today was a proud feeling and it was great to captain a good bunch of boys."
Jude Soonsup-Bell struck four goals on the day.
Bate added: "I have to give a big shout out to Jude, he stepped up to lead the line and has been on fire for the Under-18s this season so I'm not surprised with his goals."