Final answer:
Andrew Jackson's informal "cabinet," which included Martin Van Buren, was famously known as 'The Kitchen Cabinet.' This group of advisors was instrumental in aiding Jackson with key decisions on public policy after the Eaton affair.
Step-by-step explanation:
The nickname of Andrew Jackson's informal "cabinet," which included Martin Van Buren, is The Kitchen Cabinet. The "Kitchen Cabinet" was an influential group of Jackson's political friends and advisors who did not hold official cabinet positions but had significant influence on his decision-making. This group emerged following the Eaton affair and contributed to Jackson's shift away from relying on his official cabinet members. As president, Jackson used this group of advisors to help him make important decisions regarding public policy issues such as Indian removal, tariffs, and the national bank.