The easiest way to fix a burnt cake is to simply scrape off the burned edges. Whether it's the top, bottom, or sides, use a knife to gently trim off that particular part.
After scraping off the burnt edges, you must brush some sugar syrup all over it.
If your cake still looks burnt or has an odd flavour to it, then some frosting will be your best companion.
Another interesting way of fixing a burnt cake is to make delicious cake pops out of it.
If nothing else works or you're short on time to frost it or make cake pops, consider serving your cake along with some beverages such as tea or coffee.