This is kind of funny. The wonders of the Internet are bringing Azcue's together.
For those who are interested, there is a web site that publishes histories of Basque names, and Azcue is included. The link is:http://www.buber.net/Basque/Surname/A/azkue.html
It traces the Azkue name back to 1477, with Juan Ruiz Azkue. Apparently there are four coats of arms for Azcue.
My family is from the village, Mutriku (Motrico in Spanish), mentioned in the web site. My understanding is that several generations back my great-great grandfather and grandmother moved there from Lastur. In the 1920's and 1930's jai-alai became popular around the world, including Miami, Cuba, Mexico, and even China. Other Azcue's may have come to the "New World" with the Jesuits, with merchants and sailors, and with the exodus of sheep herders to southwestern United States in the 1920's and 1930's.
The Azcue claim to fame in the U.S. probably comes with Joe Azcue, a Cienfuegos, Cuba-born former major league catcher from 1960-1972 who played mainly with the Cleveland Indians.