We study the degree to which quantum entanglement survives when a three-qubit entangled state is copied by using local and non-local processes, respectively, and investigate iterating quantum copying for the three-qubit system. There may exist inter-three-qubit entanglement and inter-two-qubit entanglement for the three-qubit system. We show that both local and non-local copying processes degrade quantum entanglement in the three-particle system due to a residual correlation between the copied output and the copying machine. We also show that the inter-two-qubit entanglement is preserved better than the inter-three-qubit entanglement in the local cloning process. We find that non-local cloning is much more efficient than the local copying for broadcasting entanglement, and output state via non-local cloning exhibits the fidelity better than local cloning.