I hope you can find it in your heart to forgive me.
我希望你从内心里能原谅我。
I am sure this mistake won't happen again.
我肯定这种错误不会再发生了。
This was a mistake caused by……
这个错误完全是由于……造成的。
Business Emails 商务邮件:
Dear Zhou Wei,
I'm sorry for our disagreement this morning. I was wrong to be so angry with you about the way you have written the report. I didn't consider your point of view and I was unfair. I don't know what I can do to make it up to you, but I hope you can find it in your heart to forgive me.