An early printed example is in the newspaper article Berlin is Easy for the Western Mail 12 September 1940: The phrases “cakes and ale” (in England) and “cake and cheese” (in Scotland) have been used since the early 1600s as metaphors for the good things in life. a piece of cake.” The OED’s first citation comes from a collection of light verse by Ogden Nash, The Primrose Path (1935): “Her picture’s in the papers now, / And life’s a piece of cake.” Something easily accomplished, as in “I had no trouble finding your house-a piece of cake”. This expression originated in the Royal Air Force in the late 1930s for an easy mission, and the precise reference is as mysterious as that of the simile easy as pie. Possibly it evokes the easy accomplishment of swallowing a slice of sweet dessert. Here’s its earliest incarnation, from John Heywood’s Proverbs and Epigrams (1562): “Wolde ye bothe eate your cake, and haue your cake?”

As the OED explains, cake is associated figuratively, especially by children, “as a ‘good thing,’ the dainty, delicacy, or ‘sweets’ of a repast.”A comment of another kind from a young air gunner was: "Compared with some other places in Germany, going to Berlin was a piece of cake.” The choice of cake or pie as a symbol of ease and pleasantry is well represented in the language. Other phrases along the same lines include 'as easy as pie', 'a cake-walk', 'that takes the cake/biscuit'. Similarly, the 19th-century American expression “ *to take the cake” means “to carry off the honours, rank first,” the OED says, adding that it’s “often used ironically or as an expression of surprise.”

The Oxford English Dictionary doesn’t comment on the difficulties of cake-making, but it agrees with you that the colloquial phrase “a piece of cake” refers to “something easy or pleasant.” The AHD has a different suggestion, as you noted, as to its origin, but both sources see its earliest usages from the ‘30s. I’d point out that the supporting idea is the same:Vocabulary.com suggests that the origin of "cakewalk" is much older and includes the following definition This phrase is of American origin. At least, the earliest citation of it that I can find is from the American poet and humorist Ogden Nash's Primrose Path, 1936: The Americanism cakewalk, used to mean "something easy," came first, in the 1860's — piece of cake wasn't used until around 1936. Both cake and pie have a long history in the United States as metaphors for things that come easily.