A generic odd number can be written as

Since there is an odd number every two numbers, three consecutive odd numbers will be

Now let's make up the equations: the sum of the first two is

And 27 less than 3 times the largest is

These two must be the same, so we have

Subtracting 4k and 3 from both sides gives

Which means that the problem has no solution.
To confirm this hypothesis, we can observe that, on the left hand side, we have the sum of two odd numbers, which is even
On the right hand side, we have an odd number, multiplied by 3 (still odd), take away 27 (still odd).
So, the left hand side is even, and the right hand side is odd. They can't be the same number.