To date, historians know of three different people named Marcus Aurelius Apicius. Which one of them is the "real" Apicius is uncertain. The most famous, though, is the one who (posthumously) wrote a cookbook. Historical accounts are somewhat sketchy, but the Apicius we are talking about was born 25 BC and lived until 37 AD, during the reign of the emperors Augustus and Tiberius. He was the first to inspire a book on high-class Roman cuisine, the "De re coquinaria" or "On Cooked and Baked Things" which was published in the 4th century and consisted of a collection of Apicius' recipes. His other work is the preceding "De condituris" ("On Condiments"), a book on sauces which was absorbed into "De re coquinaria". The latter is one of the oldest cookbooks existing to date.
Marcus liked living the high life and strove to always find more exotic or just plain weird concoctions, such as nightingale tongue, pickled pig's brains or (I kid you not) stuffed sterile sow's womb. By Seneca the Younger's account, his tragical end was caused by the realization that in the end his fortune only consisted of a mere 10 million sesterces (making him by today's exchange rates still only a paltry multi-millionare), which led to him taking his own life by poisoning.
Some people are just never satisfied.
Several online booksellers offer a translated version of "De re coquinaria". Search for "Apicius" or "Roman Cookery".