Tennis, but it is actually called the Hopman Cup.
http://hopmancup.com/
The Bledisloe Cup is associated with the sport of rugby.
The America's Cup is associated with the sport of sailing.
The Americas Cup is associated with sailing.
The American Cup is associated with U.S. soccer.
"Shivanthi Gold Cup" is associated to "Volleyball".
Tennis is the sport associated with the Davis Cup.
Hockey
England football
Tennis :P
hockey
The Beighton Cup is associated with field hockey.
The UEFA Europa League, formerly known as the UEFA Cup, is associated with the sport of soccer.