Don Juan is widely considered Lord Byron's masterwork. It is comprised of 18 cantos and, in total, is one of the longest poems of any kind in English. Here is an essay that got an 18/20 in AP English that deals with whether or not Don Juan is nihilistic. Please do not copy it as I would not want to be involved in academic collusion. (Note, also, that Don Juan is pronounced in the English fashion "Don Jew-on" because of Byron's meter and, perhaps, to increase the satire).

The essence of nihilism is the absence of hope. That, despite all efforts to the contrary, life will remain in its present, horrid state. In Don Juan, Byron does imply that the present is, indeed, horrid; however, he does not imply that there is no hope. Instead, he simply states the problems of present day society and leaves improving them as an exercise for the reader.

The Ottava Rima structure of Don Juan lends itself spectacularly to satire; however, Byron does not use the form to eliminate hope--as a nihilist would--but instead uses it to point out the flaws of the present. Choosing Ottava Rima as the form for Don Juan was a brilliant move; the form well fits Byron's witty, carefree compositional style. While the sestet provides ample space for Byron's witticisms, it is the ending couplet that allows him to compose such lines as: "I say--the future is a serious matter--/And so--for Godsake--Hock and Soda water" and "He learn'd the arts of riding, fencing, gunnery,/And how to scale a fortress--or a nunnery." In Don Juan, Byron uses witticisms such as these to satire "all that was held sacred" in European Society. From marriage to the poetic theories of his contemporaries, almost nothing is safe from his satirical wit. However, this satire is not complete. If Don Juan was truly nihilistic, nothing would be safe from satire; true courage, true altruism, true prayer, all these "righteous" things would be satirized as well. However, this is not the case. For example, towards the end of Canto 3, Byron writes about prayer:

But set those persons down with me to play
And you shall see who has the properest notion
Of getting into Heaven the shortest way.

What Byron is satirizing is false prayer. Nowhere in Don Juan will you see him satire truly righteous things. Hypocrisy, avarice, lust, these things he attacks; truth is safe. For Byron, the hypocrisy described in Don Juan is, indeed, "life" but there is still hope for these, righteous, truths.

While many poetic techniques are used throughout Don Juan, the most resounding is Byron's use of parentheses and asides to point out faults; however, in pointing out these faults he does not label them insurmountable--as a nihilist would do--but, instead, merely identifies them as "abuses of the present state of society." For example, in Canto 1 he writes:

...in her as natural
As sweetness to the flower, or salt to ocean
Her zone to Venus, or his bow to Cupid,
(But this last simile is trite and stupid).

In these lines he uses the parentheses stylistically to demonstrate precisely the hypocrisy that Don Juan satirizes. Byron could easily have fixed the "trite and stupid" simile. Instead, he leaves the simile in to show that, yes, there are problems in todays society; however, just like this flawed line, these problems are not insurmountable--some are even trivially easy to overcome.
There is no explicit meaning to be found in the story of Don Juan; instead, the meaning of the poem lies in those--now fallen--ideals that Byron satirizes. Throughout the poem, Byron satirizes everything that he finds to be false, everything that has strayed from its original, true, intent and become hypocritical. He satirizes marriage:

Wedded she was...to a man
Of fifty...
And yet, I think, instead of such a ONE
'Twere better to have TWO of five and twenty.
He satirizes the overall fate of women:
...for man, to man so oft unjust,
Is always so to women...
...their bursting hearts despond
...till some wealthier lust
Buys them in marriage--and what rests beyond?
A thankless husband, next a faithless lover,
Then dressing nursing, praying, and all's over.

In each case he demonstrates that a former grand truth has degraded into hypocrisy. The true meaning of the poem is the antithesis of these hypocrisies: the truths themselves. If Byron was nihilistic, he would have declared the institutions themselves inherently false, for a nihilist believes in nothing. Instead, Byron makes Don Juan the "most moral of poems" by declaring the hypocrisies that the institutions have become as false, not the righteous institutions themselves.

At first ridiculed as completely immoral, then tossed aside as morally nihilistic, in the end it can easily be seen that Byron was at least partially correct in his assessment of Don Juan as the "most moral of poems." Whiler perhaps not the "most" moral, by ridiculing the hypocrisy of many "truths" Don Juan proposes that--sans the hypocrisy society has replaced them with--the truths themselves are still worthy. Essentially, in each case Byron satirizes the falsehood that had replaced the truth; he satirizes the hypocrisy but does not satirize the truth itself. Calling Don Juan morally nihilistic is to focus solely on the concept that Byron does satire and to ignore the hypocrisy that concept has become..