Quote"Sextus Empiricus was a Pyrrhonian Skeptic living probably in the second or third century CE, many of whose works survive, including the Outlines of Pyrrhonism, the best and fullest account we have of Pyrrhonian skepticism (a kind of skepticism named for Pyrrho (see entry on Ancient Skepticism)). Pyrrhonian skepticism involves having no beliefs about philosophical, scientific, or theoretical matters—and according to some interpreters, no beliefs at all, period."
It looks like there is a possibility that Sextus Empiricus could be the possible source of the "Epicurean paradox" or "Epicurean dilemma". Doing a quick Google search you find it sometimes stated as some kind of fact that it was written by Epicurus. However, no extant writings of Epicurus contain this argument and it is possible that it has been misattributed to him.
"The “Epicurean paradox” is a version of the problem of evil. Lactantius attributes this trilemma to Epicurus in De Ira Dei:
"God, he says, either wishes to take away evils, and is unable; or He is able, and is unwilling; or He is neither willing nor able, or He is both willing and able. If He is willing and is unable, He is feeble, which is not in accordance with the character of God; if He is able and unwilling, He is envious, which is equally at variance with God; if He is neither willing nor able, He is both envious and feeble, and therefore not God; if He is both willing and able, which alone is suitable to God, from what source then are evils? Or why does He not remove them?"
"Perhaps the earliest expression of the trilemma appears in the writings of the sceptic Sextus Empiricus (160–210 AD), who wrote in his Outlines of Pyrrhonism:
"Further, this too should be said. Anyone who asserts that god exists either says that god takes care of the things in the cosmos or that he does not, and, if he does take care, that it is either of all things or of some. Now if he takes care of everything, there would be no particular evil thing and no evil in general in the cosmos; but the Dogmatists say that everything is full of evil; therefore god shall not be said to take care of everything. On the other hand, if he takes care of only some things, why does he take care of these and not of those? For either he wishes but is not able, or he is able but does not wish, or he neither wishes nor is able. If he both wished and was able, he would have taken care of everything; but, for the reasons stated above, he does not take care of everything; therefore, it is not the case that he both wishes and is able to take care of everything. But if he wishes and is not able, he is weaker than the cause on account of which he is not able to take care of the things of which he does not take care; but it is contrary to the concept of god that he should be weaker than anything. Again, if he is able to take care of everything but does not wish to do so, he will be considered malevolent, and if he neither wishes nor is able, he is both malevolent and weak; but to say that about god is impious. Therefore, god does not take care of the things in the cosmos."
Source: Lectures Bureau