When making a mistake at work is it best to admit your fault & attempt to rectify it or say nothing & cover up your mistake?

Admit your fault! You do not lose anything by admitting your mistakes. And you will gain immensely, by not committing the mistake again and you will correct it. And you can be role-model for others. Don't cover up, because it is cowardice and suicidal.

Always admit your fault with anthusiasm and convience your superiors that it won't happend again with positivity so that it will help to increase trust level .

Ethically one must admit his fault and i think this is the best practice

Admit fault and rectify is the responsible answer. To cover up will always resurface later and make you not only look unprofessional but also untrustworthy. To admit your mistake shows confidence in your position and that the company's success matters to you. Always have a suggestion of how to rectify when you admit it to show your abilities to problem solve with maturity.