David slung a stone from his sling; it sank into Goliath's forehead, and he fell to the earth. David followed this up by standing on Goliath and cutting off his head with the giant's own sword.

David killed Goliath with a stone.

There is absolutely no source literature, not from the Early Church Fathers or any other source, which states that Goliath's head was buried at Golgotha.

And David took the head of the Philistine, and brought it to Jerusalem; but he put his armour in his tent. 1.Sam 17,54

According to this scripture, the head of Goliath was brought to Jerusalem. What happened to the head after this is never mentioned.

1 Samuel 17:50, 51 - So David prevailed over the Philistine with a sling and a stone, and struck the Philistine and killed him. But there was no sword in the hand of David. Therefore David ran and stood over the Philistine, took his sword and drew it out of its sheath and killed him, and cut off his head with it. And when the Philistines saw that their champion was dead, they fled. [NKJV]

He made one marble David and one bronze David. In both cases David is standing on the severed head of Goliath.