Harry Potter and the Prisoner of Azkaban chapter 1 describes the first six weeks of Harry's second summer holidays, which he's spent at the Dursley's home at Privet Drive. It specifically says that he has his cauldron there in a cupboard.
The most the Dursleys could do these days was to lock away Harry's spellbooks, wand, cauldron and broomstick at the start of the summer holidays, and forbid him to talk to the neighbours.
Now, Harry has bought this cauldron two years ago, and uses it at Hogwarts every year for Potions lessons. There seems no chance that he's use the cauldron for anything during the summer holidays. Why did he take the cauldron home, rather than leaving it in Hogwarts?
I can mostly understand why he took his other possessions. The owl Hedwig needed care and served as company for him, he needed his spellbooks to write homework, and I can understand why he wouldn't want to part from his wand or the Nimbus Two Thousand rancing broom, which is described as “one of Harry's most prized possessions” in the same chapter. But none of this applies to his cauldron.