well, the netstat command can only help you in identifying the process, the port it listens on and from who does it accept packages.
I can only help you with understanding the output.
udp - the protocol it accepts (it can recieve only udp packages)
1740 - "The count of bytes not copied by the user program connected to this socket." (quote from the man page) - this might suggest a buffer overflow, or the fact that it is still reading and processing the package. Check if the number changes.
0 0.0.0.0:6060 - it accepts packages with any destination if they reach the port 6060 on this computer
0.0.0.0:* - it accepts packages from any computer
0 - it runs as root
23093916 - the program's inode
21961/java - this is the pid and the application of the program listening on this port.
So, are you running any java program? Check the processes you are running, and find out what the problematic program is. This might help http://www.cs.columbia.edu/~akonstan/javaps/
If you find it, see if you really need it. If not, you can disable it. Otherwise, upgrade it, if you are sure there is a security issue. It might be solved in the next release.