Adweek magazine - recent and back issues are available within various third party business article databases. This link to Adweek magazine will bring up the access available from Ebsco's Business Source Elite database (1994 - present).
To arrive at the point manually, begin that access by typing "Adweek" into the library's journals a to z list. Scroll beyond some partial coverage of regional copies of Adweek to the entry depicted in the image below - for the main U.S. edition of Adweek. Click though the link labeled "Business Source Elite" for the coverage that comes closest to the current date. The access point for ABI/Inform is an alternative option (2004 - recent issues; but less current than the Business Source Elite access).
Adweek also offers student discounts for personal digital subscriptions.