the 3 consecutive numbers can be written as

x-1, x , x+1 with x-1 the smallest

their product is 161 larger than the cube of the smallest

(x-1)x(x+1) = 161 + (x-1)^3

by solving we find and consider the positive roots

x = 8

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x - 1 = 8 - 1 = 7

x + 1 = 8 + 1 = 9

the numbers are 7, 8 and 9.