When you cut a pothos, it may "bleed" for a few hours at the most, but I've never heard of them leaking for a week! The cuts should have healed within a few hours. Keep this in mind: Golden Pothos are part of the Arum family, which has poisonous sap. So be careful.
Well, I've heard of "guttation". This means that when a
plant absorbs more water than it needs, the water can be expelled out of leaf tips. Though I've never had this happen to me before, it is a possiblility. Make sure the
plant is not overwatered!
Otherwise, I've no idea why it would be leaking for this long.