What is n squared plus thirty two if six hundred eighty times ninety cubed?

Here's how to solve this problem step-by-step:

1. Calculate 90 cubed: 90³ = 90 * 90 * 90 = 729,000

2. Calculate 680 times 90 cubed: 680 * 729,000 = 495,720,000

3. The problem states this result is equal to n² + 32: Therefore, n² + 32 = 495,720,000

4. Solve for n²: Subtract 32 from both sides: n² = 495,720,000 - 32 = 495,689,968

Therefore, n² = 495,689,968. The question doesn't ask for the value of 'n', only n².