book Maths Puzzle Numerical Ability

The directions say to factor as completely as possible
(x-5)^3 -1

The answer is (x-6) (x^2 -9x +21)

I cannot figure out how to get this answer. Can you please show the steps?

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book Other Question

One number is five times another number. If the sum of two numbers in 270, find the numbers
Three times a number, decreased by 8 is the same as twice the number, increased by 15?Find the number.