Q:

My employee make some error mistake in finance report (not update excel formula) and I am answerable to my superior

I previously, put together an important financial report for my boss with minimal errors.  I have since delegated this function to an employee, but they failed to update a formula, with big consequences.  
Please note that I caught some errors in this report, but did not catch the formula issue.  My boss, however, did, and is holding me responsible. 
How should I deal with this situation in regards to my own career, and my employee? 

A:

I'll assume that you've already fixed the issues that your boss found and done a thorough check that the report is now correct.   If you haven't done that, that's the first order of business. 
After that,

Take responsibility for the mistake.   It's your team, so you get the blame when the team makes a mistake (but you also get the credit when the team delivers successfully).   This means that you'll need to apologize to the boss for the mistakes. 
Understand why the mistake was made.   It's possible that the person you delegated the report to ignored multiple verbal and written instructions to update a formula.   On the other hand, I have seen more than my fair share of Excel spreadsheets that were being used to deliver important reports that were a poorly designed mess that could never realistically be understood by anyone other than the original author and would never produce results that could be reconciled to the actual source systems.   When I hear that a formula had to change, I automatically suspect that there are substantial opportunities to make the spreadsheet more user-friendly. 
Present a plan for preventing the mistake from happening again.   Perhaps that means that you have to do it which may mean that something else has to be delegated or dropped.   Perhaps that means that the employee needs additional training or the process of preparing the report has to be documented better or the report needs to be reconciled to some other system before it is sent out.   Maybe you need to work with your organization's IT department to build the report in a way that requires much less manual intervention.   Present that plan to the boss.   A good boss should be happy to have people make mistakes-- that means that they're trying to do new things-- so long as they learn from them and don't repeat them. 

A:

It is entirely reasonable that your boss hold you responsible for the work being done in your name, and it's also reasonable that you hold you employee responsible for their quality of work. 
You're in a management/leadership position, and, I presume, quite busy, which is why you delegated this work to someone else.  This person did a poor job of it, which is clearly a problem.  However, you failed to catch those issue before passing the work on to your own superior, which is your mistake.  
So now you boss is demanding answers, and rightly so.  There's several issues I see:

You need to fix the report ASAP
You need to own up to your mistake
You need to deal with your errant employee

Don't simply get angry at this employee - understand why the mistake was made.  Was it due to a lack of training, knowledge, or understanding?  If so you need to provide that training! 
Was it due to laziness, or lack or attention to detail?  In that case you need to have a serious talk with this person and make sure that this will never happen again.  Better supervise this person.  Maybe put aside some time to give this person periodic feedback so that their performance improves. 
Either way, you should apologise to your boss, take responsibility for what happened, promise that it never will again, and then make damned sure it never does.