Wet spot on outside of foundation oozing
My guess is that a lump of unmixed something-or-other made it into the concrete pour. If it was portland cement it would have cured long ago, so maybe it's lime, which is added to concrete as a flex and waterproofing agent.

Lime concrete, produced by this mix, makes a good base for load bearing walls, columns, or laying under floors because it has a degree of flexibility that regular concrete does not. It also has a certain waterproof property to it that prevents subsoil dampness in floors and walls. Additionally, lime concrete can be made easily and cheaply while still providing a durable material that resists weathering and wear and tear.
http://www.doityourself.com/stry/how-much-lime-should-i-add-to-a-concrete-mix