Yes, all bases specifically all Lewis bases are nucleophiles.
Nucleophiles are chemical species which have a pair of electrons to donate to an electrophile.
Since Lewis bases have a pair of electrons to donate, all Lewis bases are nucleophiles.
However their is a little difference between bases and nucleophiles is that nucleophilicity is the tendency to attack on the Carbon atom while basicity is the tendency to attack on hydrogen atom bonded to Carbon molecule.
The above points clearly explains the difference and similarity between bases and nucleophiles.