The one place you will find the marketing expenses for companies is in their annual reports or 10-K filings.
Apple has not traditionally produced a print annual report like other companies do, but you can get to their 10-K reports from EDGAR files or this page: https://investor.apple.com/investor-relations/default.aspx
You should search for the line item Accrued Marketing and Selling Expenses. This will include marketing, promotions, advertising, and sales force expenses, but it is as close as you will get to the "marketing" budget. For competitors search for their corporate website (search on company name and corporate) and look on their Investor Relations page for their annual report which is typically in a pdf format.
Additionally, publicly traded companies should have their financial information available on databases like D&B Hoovers.
Apple is not a company to disclose much, so identifying their advertising agency, and generally finding much information about the company is not easy, however it may be possible to find information from articles and news sources in the library's databases such as Business Source Complete.
