Fluffy resembles Cerberus, another giant, 3-headed dog. This is how it’s described in The Aeneid, where Aeneas and the Sybil are entering the underworld (p.196, translated by Robert Fagles):

“These

are the realms that monstrous Cerberus rocks with howls

braying out his three throats, his enormous bulk,

squatting low in the cave that faced them there.

The Sybil, seeing the serpents writhe around his neck,

tossed him a sop, slumbrous with honey and drugged seed,

and he, frothing with hunger, three jaws spread wide,

snapped it up where the Sybil tossed it - gone.

His tremendous back relaxed, he sags to earth

and sprawls over all his cave, his giant hulk limp.

The watchdog buried now in sleep, Aeneas seizes

the way in, quickly clear of the river’s edge,

the point of no return.”

I like Rowling’s way of getting Potter around Fluffy (playing a song on a flute that causes Fluffy to go to sleep) better than Virgil’s way of getting Aeneas around Cerberus (a drugged seed that causes Cerberus to go to sleep). My guess is that Rowling took inspiration from how Orpheus (in another story) got around Cerberus (by playing his lyre, which caused Fluffy - I mean, Cerberus - to go to sleep).

Not surprisingly, after Potter gets by Fluffy, he then descends to an underworld … Hmmm …