/usr/share/tomcat8/lib/tomcat-api.jar is in tomcat8-common 8.0.32-1ubuntu1.
This file is owned by root:root, with mode 0o777.
It is a symlink to /usr/share/tomcat8/lib/../../java/tomcat8-api.jar
/usr/share/tomcat8/lib/../../java/tomcat8-api.jar