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Mathematical induction does not know how to extract factors.
When n= 1, left = 2 3 = 8, right =2*4=8.

When n=n+ 1, an item [2 (n+ 1)] 3 is added to the left.

=(2n+2)^3

=8n^3+24n^2+24n+8…………………………………( 1)

Right = 2 (n+ 1) 2x (n+2) 2

Added 2 (n+1) 2x (n+2) 2-2n2x (n+1) 2.

=2[(n+ 1)^2x(n+2)^2-n^2x(n+ 1)^2]

=2(n^2+2n+ 1)[(n^2+4n+4)-n^2]

=2(n^2+2n+ 1)(4n+4)

=2(4n^3+8n^2+4n+4n^2+8n+4)

=2(4n^3+ 12n^2+ 12n+4)

=8n^3+24n^2+24n+8…………………………………(2)

( 1)=(2)

Established.