Can an outside socket be used to run electricity to an outdoor kitchen area (about 20 ft away) and then to an outdoor shed (about 60 ft away)?
CAN it? Well soitanly. Out here in redneckville us folks string extension cords all over tarnation all the time. ain't no problem 'til the tractor runs 'em over a few times, then they go all sparkin' and blowin' fuses and annoyin' the wifey.
However, CAN and SHOULD are different terms.
We're going to need more information in order to provide you a proper answer, but "outdoor kitchen area" plus "shed" sounds like it could add up to more than one circuit... and we don't even know what else is on the same circuit as your "outside socket".
Describe your "outdoor kitchen area" - what you're looking to put there for electrical stuff. Is this a charcoal grill you want to put a single outlet next to so you can plug in your radio for some tunes while you barbecue, or are you installing a full commercial kitchen on the patio? Also describe the shed. Are we talking a little tiny storage shed you want to put a light bulb in, or a massive workshop kind of thing?