The giant who owns the cauldron needed for brewing mead for the gods is Hymir.
In the Old Norse poem Hymiskviða, the gods decide that Ægir, a master brewer, should host a feast for the Æsir. Ægir agrees only if they can provide a vessel large enough to brew beer for everyone. Týr remembers that his father, the giant Hymir, owns a remarkably large cauldron.
Thor and Týr travel to Hymir's home to obtain it. The visit includes several famous episodes: Thor eats an extraordinary amount of food, joins Hymir on a fishing trip, and nearly catches Jörmungandr, the Midgard Serpent. Thor later proves his strength by smashing a magical drinking vessel against Hymir's unusually hard head.
Hymir is sometimes confused with Suttungr, who is connected to the Mead of Poetry, a different mythic drink associated with Odin. The cauldron in this story is a brewing vessel for Ægir's communal feast, not the container of Kvasir's poetic mead.