Where is Ogden Nash's "piece of cake"?

So the book arrived today and I found the sentence, exactly on the page stated in 1006a's answer (page 172). I added some more links to photos at the end of my answer.

I also recommend reading the comments (both on the question and the answers), there are some interesting references to earlier versions of the poem in which "And everything is jake" took the place of "And life's a piece of cake". It remains unclear whether the change was made by the author himself or a (British) editor.

The poem starting at 'Mrs. Sonia Katzenstein':

Links to full-size photos

First page of the full verse

Second page of the full verse

Freud poem

Title page

Publication information

Attribution: Nash, Ogden. The Primrose Path. London: Bodley Head, 1936.

Ogden Nash was a twentieth-century American poet, who authored over 500 poems. One of his books of poems was The Primrose Path,

The OED seems to be the source of the original citation of Nash's The Primrose Path as the earliest identified figurative use in print of "piece of cake". The online entry for piece¹ includes, under Phrases, this entry and attestation:

piece of cake n. colloq. something easy or pleasant.
1936 O. N_^ASHPrimrose Path 172 Her picture's in the papers now, And life's a piece of cake.

The citation details given are

Ogden Nash · The primrose path · 1936.
London

According to WorldCat (an online catalog of libraries around the world), there were at least two editions, one published in 1935 in New York by Simon & Schuster and the other in 1936 in London. They seem to be rather different; the US edition is 354 pages of apparently all original works, while the UK edition is listed as a slim 218 pages and apparently contains "A selection from 'The primrose path' & 'Happy days': also a few other verses ..." (although the WorldCat entry for that version lists 354 pages).

These differences may explain why, of the twelve words and phrases that the OED attributes to Primrose Path, I was only able to locate six in the 1935 book, not including "piece of cake".² Of these, only one was on the page listed; the rest were randomly redistributed. On page 171, which is the cited page for the "piece of cake" quotation, there is a poem "The Strange Case of Professor Primrose" about an absentminded professor who accidentally becomes a Pullman Porter.

Interestingly, where the OED has "tank" (of beer) the version I have has "mug". This is similar to the "derby"/"bowler" difference raised in the original question. If Nash's British editors made a practice of suggesting (or unilaterally making) changes to the text, perhaps to make it more accessible to British readers, that could explain how an allegedly British phrase turned up in a book of poems by an American author.³

¹_{"piece, n." OED Online, Oxford University Press, January 2018, www.oed.com/view/Entry/143547. Definition P.15. Unfortunately, the OED is a subscription service; many people, including most UK residents, can access the OED online through their local or institutional library. Check with your librarian for more information.}

²_{Clicking on the link to "find more citations from Primrose Path" leads to quotations for the following twelve words and phrases; my findings or lack thereof are in parentheses:}

1. _{Adamless, adj. 1936
   ...1936 O. Nash Primrose Path 218 Lonely Eve in an Adamless Eden. (Not located)}
2. _{beskirted in be-, prefix 1936
   ...1936 O. Nash Primrose Path 165 And all the trim and not so trim ladies who have been be-trousered begin thank God once more to be be-skirted. (Not located)}
3. _{beep, v. 1936
   ...1936 O. Nash Primrose Path 101 Beep the horn and howl the klaxon For Hebrew, Latin and Anglo-Saxon; Howling klaxon, beeping horn. (YES, “Beat That Light”, p. 343)}
4. _{divot, n 1935
   ...1935 O. Nash Primrose Path 1936 105 The wretched golfer, divot-bound. (Not located)}
5. _{hellgrammite, n. 1935
   ...1935 O. Nash Primrose Path 1936 122 This human hellgramite that I think we could all dispense with. (Not located)}
6. _{over-inflate, v. 1936
   ...1936 O. Nash Primrose Path 14 Jonathan over-inflates his lungs. (YES, “Tell It to the Esquimos, or Tell It to the Esquimaux”, p. 60)}
7. _{phooey, int., adj., and n. 1936
   ...1936 O. Nash Primrose Path 185 And I'll say, ‘Phooie!’ or something of the sort. (Not located, but there is a poem entitled "Weather Clear, Track Fast, Horses Phooie!" on p. 303)}
8. _{piece of cake in piece, n. 1936
   ...1936 O. Nash Primrose Path 172 Her picture's in the papers now, And life's a piece of cake. (Not located)}
9. _{setting-up exercise in setting, n.¹ 1935
   ...1935 O. Nash Primrose Path 37 A few setting-up exercises. (YES, “There Is No Danger Line”, p. 37)}
10. _{symbol-minded in symbol, n.¹ 1936
    ...1936 O. Nash Primrose Path 55 Still, I think, a pig's a pig—Ah, there, symbol-minded Sig! (YES, “Sigmund Freud”, p. 141)}
11. _{tank, n.⁸ 1936
    ...1936 O. Nash Primrose Path 46 What can a man..Ask..More than a pipe..And a modest tank of beer? (SORT OF, “Home, 99 44/100 % Sweet Home”, p. 117: What can a man, can a family man Ask in the way of cheer More than a pipe, and a reading lamp, And a modest mug of beer?)}
12. _{third baseman in third adj. (and adv.) and n. 1936
    ...1936 O. Nash Primrose Path 38 Long have I wondered why a locomotive engineer should be so much nicer than an ambassador or a novelist or a banker or a third-baseman or a quartermaster or a lancer. (YES, “Ding Dong, Toot Toot, All Aboard!”, p. 108)}

³_{In fact, @Sven Yargs was able to track down a very similar line to the OED's "piece of cake" quotation, but without the phrase in question:}

_{Her picture's in the papers now, And everything is jake.
—Ogden Nash, Many Long Years Ago, 1941 (snippet view)}