Harry's wealth is mentioned extensively throughout the book series and at least once (and usually several times) in each book.
HP and the Chamber of Secrets
Harry said nothing. He felt a bit awkward. Stored in an underground
vault at Gringotts in London was a small fortune that his parents had
left him. Of course, it was only in the wizarding world that he had
money; you couldn’t use Galleons, Sickles and Knuts in Muggle shops.
He had never mentioned his Gringotts bank account to the Dursleys; he
didn’t think their horror of anything connected with magic would
stretch to a large pile of gold.
Harry felt even worse when they reached his vault. He tried to block
the contents from view as he hastily shoved handfuls of coins into a
HP and the Prison of Azkaban
Once Harry had refilled his money bag with gold Galleons, silver
Sickles and bronze Knuts from his vault at Gringotts, he needed to
exercise a lot of self-control not to spend the whole lot at once. He
had to keep reminding himself that he had five years to go at
Hogwarts, and how it would feel to ask the Dursleys for money for
spellbooks, to stop himself buying a handsome set of solid gold
Gobstones (a wizarding game rather like marbles, in which the stones
squirted a nasty-smelling liquid into the other player’s face when
they lost a point).
HP and the Goblet of Fire
‘The gold I gave you at the Quidditch World Cup,’ said Ron. ‘The leprechaun gold I gave you for my Omnioculars. In the Top Box. Why didn’t you tell me it disappeared?’
Harry had to think for a moment before he realised what Ron was talking about.
‘Oh …’ he said, the memory coming back to him at last. ‘I dunno … I never noticed it had gone. I was more worried about my wand, wasn’t I?’
They climbed the steps into the Entrance Hall and went into the Great Hall for lunch.
‘Must be nice,’ Ron said abruptly, when they had sat down and started serving themselves roast beef and Yorkshire puddings. ‘To have so much money you don’t notice if a pocketful of Galleons goes missing.’
HP and the Order of the Phoenix
Harry grinned. He had forced the Weasley twins to take the thousand
Galleons prize money he had won in the Triwizard Tournament to help
them realise their ambition to open a joke shop, but he was still glad
to know that his part in furthering their plans was unknown to Mrs
Weasley. She did not think running a joke shop was a suitable career
for two of her sons.
Harry Potter and the Half-Blood Prince
Bill, who would be staying at home with Fleur (much to Hermione and Ginny’s pleasure), passed a full money-bag across the table to Harry.
‘Where’s mine?’ demanded Ron at once, his eyes wide.
‘That’s already Harry’s, idiot,’ said Bill. ‘I got it out of your vault for you, Harry, because it’s taking about five hours for the public to get to their gold at the moment, the goblins have tightened security so much. Two days ago Arkie Philpott had a Probity Probe stuck up his … well, trust me, this way’s easier.’
‘Thanks, Bill,’ said Harry, pocketing his gold.
Harry Potter and the Deathly Hallows
Gringotts had seemed a place of wonder that day, the enchanted
repository of a trove of gold he had never known he possessed, and
never for an instant could he have dreamed that he would return to
steal … But within seconds they were standing in the vast marble hall
of the bank.