The phrase boys will be boys is used to express resignation regarding an undesirable aspect of the behaviour of a boy or young man, as being supposedly characteristic of his age or sex.
—Cf. also the phrase girls will be girls.

These are, in chronological order, the earliest occurrences of the phrase boys will be boys that I have found:

1-: From The Apothecary’s Defence of Dr. Bentley, in Answer to the Spy. Together with some Observations, Moral and Critical, upon the Fable of the Jack-daw in Peacock’s Feathers; Particularly address’d to the Author of the Spy (London: Printed for J. Roberts, 1721):

As it happens that Doctor Bentley’s Studies are rais’d above the Level of the Spy’s Capacity, so his Productions, of consequence, are out of the Reach of his Criticisms. Methinks, the Spy appears to me like one of those ignorant, unlucky, Boys, who to shew their Dexterity, and keep their Hand in practise, throw Stones at, and batter those Monuments of Antiquity, which the Curious would be glad to purchase, and call their own, at an extravagant Price. But Boys will be Boys, and rashly let fly at the greatest Rarities, because they least understand their Value. And by the same Fatality of Ignorance, your juvenile, and ungrounded Smatterers in Criticism are led to cavil and decide upon the Performances of those, whose Talents are too deep for their superficial Comprehensions.

2-: From A series of genuine letters, between Henry and Frances (London: Printed (by Assignment from E. Johnston) for J. Bew, 1786), by Richard Griffith (died 1788) and Elizabeth Griffith (c.1720-1793):

Poor Jack could hardly believe the Intelligence real.—I am very sure that both the Lads shed Tears of Joy. Heavens bless them both!—though Jack is under a Cloud with me at present—but Boys will be Boys—and I endeavour to make my Philosophy like yours—severe only to itself.

3-: From Thoughts on Publick Education, published in Prose on several Occasions; accompanied with some Pieces in Verse (London: Printed for T. Cadel, 1787), by the English playwright and essayist George Colman (1732-1794):

As for their quarrels at chuck or ball, their tricks and truantries, he who breeds his son in his own family will in vain expect to see him a man before his time. Boys will be boys at home or abroad. Every age has its follies and infirmities; and those of youth and childhood, though the most innocent, are perhaps the most ungovernable.

4-: From The Two Cousins; Or, Spare the Rod and Spoil the Child (London: Printed and sold by John Marshall, 1797):

I’ll tell you what, Sarah, boys will be boys, do what we will, and it is not in their nature to like old people.

5-: From The Witch, and the Maid of Honour (London: Printed for the author, 1799), by the English writer Elizabeth Craven (née Berkeley – 1750-1828):

Nothing should remain of my great grandfather’s folly, but that great pile of stone the house; and that I love only because I was born there, and had so much pleasure in running in the galleries when I was young, and finding birds nests in the park. I remember that in the place where we now stand was a pretty run of water at that time, where I used to catch gudgeons; and many a time have I drank out of my cap here in a hot day; but that is all past and gone, and yet I remember it just as well as if it were but yesterday, and many and many a time have I slipped the greyhounds in the park at the hares when out of season, and hid those they killed; but boys will be boys. And when I was in love, I used to sit under these trees and sigh, I hardly knew why or wherefore, and was as whimsical as an ape.

6-: From a letter published in the Federal Galaxy (Brattleboro, Vermont) of Tuesday 5^th February 1799:

We have observed with concern, in reading various newspapers, no less than seven school houses consumed by fire this current winter; and it is probable many more will share the same fate before the spring. […]
[…]
[…] When the building is burnt, the carelessness of boys is always a ready standing excuse for the masters—and it is as vain to expect that any corrections or admonition given to the schollar [sic] will preserve the buildings. Boys will be boys—and we have all been boys, and recollect the thoughtlessness of our youth.