May I ask a favor of you?可以用“With pleasure”回答么？最好能给出根据

可以。

牛津高阶英汉双解词典：
with `pleasure
one is pleased to accept, agree, etc 愉快地接受、 同意等: `
Will you join us?' `Thank you, with pleasure.' ‘你愿意和我们在一起吗?’‘谢谢, 非常愿意.’
* `May I borrow your car?' `Yes, with pleasure. ' ‘我可以借用你的汽车吗?’‘可以, 很愿意借给你.’

可以

可以的，以上的答案已经很好的。用with pleasure 或 it's my pleasure

with `pleasure
one is pleased to accept, agree, etc 愉快地接受、 同意等: `
Will you join us?' `Thank you, with pleasure.' ‘你愿意和我们在一起吗?’‘谢谢, 非常愿意.’
* `May I borrow your car?' `Yes, with pleasure. ' ‘我可以借用你的汽车吗?’‘可以, 很愿意借给你.’