examine the first seven consecutive even numbers:

let 'n' represent the smallest even number, then 'n+1*2' represents the second, 'n+2*2' the third, etc. up to 'n+6*2'

n+(n+2)+(n+4)+(n+6)+(n+8)+(n+10)+(n+12)

which simplifies to 7n+42 = 7(n+6)

so a formula for any number of consecutive even numbers would be:

t(n+t-1) where 't' represents the number of consecutive numbers