What is an example of an argument that is valid but not deductively valid?

A deductive argument is one that provides a guarantee of the conclusion reached through that argument being true as long as the argument's premises themselves are true. 
So, let's look at an example:

If the Titanic hit an iceberg at 11:40 PM on April 14, 1912, then Donald Trump is a cockroach. 
The Titanic hit an iceberg at 11:40 PM on April 14, 1912.
Therefore, Donald Trump is a cockroach. 

In this example, the structure of the argument itself is valid. It follows the pattern:

If P, then Q.
P.
So Q.

Technically, this argument is valid because according to the logical setup of the argument, it is impossible for its premises to be true while its conclusion is false. That being said, this does not make it deductively sound (which I think is what you were really trying to ask in your question!), as the premises here are false. The Titanic did hit an iceberg at that time and date, but that has no connection to whether or not Donald Trump is a cockroach. Donald Trump is actually not a cockroach, but rather the Republican's candidate for President--a human being. Thus, you have a valid but unsound argument.