I am surprised that on the internet I cannot find this statement, which is more general than the Goldbach Conjecture, such as:
Any integer number divisible by integer k can be represented as the sum of k prime numbers.
Let A = k * C, | k, C ∈ N, k > 1, C > 1 | =>
∃ p1, p2, … pk that A= ∑pi where pi – prime number.
Assuming the Goldbach Conjecture to be actually true, proof of the above is easily performed by mathematical induction.