There's a lot of alliteration of "Sonnet 55," bringing the poem's images to life or echoing its ideas through sound.
The first line is packed full of sound patterning, with two separate alliterative sounds at work:
Not marble nor the gilded monuments
Here, the /n/ and /m/ are both quite soft sounds, perhaps hinting that the "monuments" being described are not as tough and durable was they might at first appear. But the specific sound isn't as important as the way that the obvious alliteration reflects the showy decoration the line describes. These attention-grabbing sounds support the speaker's criticism of "princes" who seek immortality through statues and monuments.
Those sounds contrast with the plosive /p/ in the following line:
Of princes shall outlive this powerful rhyme,
These dueling /p/ sounds contrast two different types of power in a heavyweight battle between princes and poetry. The shared sound makes this contrast more obvious, while stressing that "powerful" poetry wins every time.
The sibilant /s/ alliteration in line 4, meanwhile, sounds slippery and oily, working with the /s/ consonance of "besmeared" to make the image of "stone" tributes ruined by "sluttish time" especially vivid.
Line 10's "pace" and "praise," both of which refer to the movements and the glories of the addressee, recall the strong /p/ of "powerful" and subtly reinforce the idea that the addressee will live on after death through this poem.
In the last line, alliteration in "live" and "lovers'" links the two words together, emphasizing that as long as there are lovers in the world, this poem will be read, and the memory of the speaker's lover will survive. /L/ is what's known as a liquid consonant, and its long delicious sound is often associated with luxury and elegance. The way that /l/ moves the tongue around the mouth also perhaps gestures towards kissing—a popular lovers' activity!