Choose a number above 5 and then add odd 2 consec below and above. What is special?

Question

Choose an odd number above 5, then add 2 consecutive odd numbers below and above it. Do the same with an even number above 6. How do these compare and how do you proove with pictures and algebra?

Answer 1

let 2n+1 be odd number
2n-3+2n-1+2n+3+2n+5
=8n+4
where n>5
the min value of the sum is 52


len 2n be positive number.
2n-4+2n-2+2n+2+2n+4
=8n
where n>6

the min value of the sum is 56

Answer 2

I'm no good with algebra or pictures, but in my pea brain calculations, the number is always a multiple of 5 x the original number