Will odd numbers when added always make even numbers

Always. consider 2x which is always even (divisible by 2)

then 2x+1 is the form of all odd numbers.

add 2 of the odd numbers together to get (2x+1) (2y+1) = (4y² + 2x + 2y) + 1

the part in parentheses is always even can you see why? then adding one again always gives us an odd number.