The speaker in this sonnet is obviously Shakespeare himself. He is very confident of his genius as a poet, and he is saying that the sonnet he is in the process of creating will outlast structures made of marble and other stones. It is noteworthy that the imagery is very strongly associated with cemeteries. This suggests that the person to whom sonnet #55 is addressed has recently died and that this particular sonnet is a memorial or elegy; otherwise it would seem inappropriate to use such morbid images in a love sonnet addresssed either to a living man or woman. It would create an unpleasant impression on the person to whom the sonnet was addressed.
Shakespeare was right. His sonnet was written some four hundred years ago and has outlasted many gilded monuments of princes. Most of the buildings that existed in Shakespeare's time, with a few exceptions including Shakespeare's own home, have been destroyed by time or by war, but his sonnets are being read by millions of people, including students. The speaker in all of Shakespeare's sonnets, since they were personal and addressed to a single individual, can be assumed to be Shakespeare himself.
The most interesting metaphor in sonnet #55 is
But you shall shine more bright in these contents
Than unswept stone, besmear'd with sluttish time.
Marble headstones that have been neglected over the years acquire a dirty patina resembling a stone front step which is not properly cleaned by a sluttish housemaid. She should sweep off the accumulated dirt and then scrub it; instead she simply runs a wet mop over it and leaves it smeared with a brownish scum. It is the adjective "sluttish" that creates the metaphor.