Chapter 1.2A, Problem 5A

ASSESSMENT

The pattern $1,8,27,64,125,\mathrm{...}$ is a cubic pattern named because $1=\mathrm{1.1.1}$ or $1^3,8=\mathrm{2.2.2}$ or $2^3$, and so on.

a. What is the least 4-digit number greater than $1000$ in this pattern?

b. What is the greatest 3-digit number in this pattern?

c. What is the greatest number in this pattern that is less than ${10}^4$.

d. If this pattern was produced in a normal spreadsheet, What is the number in cell $A14$?