java.lang.NoSuchMethodError: org.apache.commons.codec.binary.Base64.encodeBase64String() in Java EE application

That method was introduced in Commons Codec 1.4. This exception indicates that you've an older version of Commons Codec somewhere else in the webapp's runtime classpath which got precedence in classloading. Check all paths covered by the webapp's runtime classpath. This includes among others the Webapp/WEB-INF/lib, YourAppServer/lib, JRE/lib and JRE/lib/ext. Finally remove or upgrade the offending older version.

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Update: as per the comments, you can't seem to locate it. I can only suggest to outcomment the code using that newer method and then put the following line in place:

System.out.println(Base64.class.getProtectionDomain().getCodeSource().getLocation());

That should print the absolute path to the JAR file where it was been loaded from during runtime.

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Update 2: this did seem to point to the right file. Sorry, I can't explain your problem anymore right now. All I can suggest is to use a different Base64 method like encodeBase64(byte[]) and then just construct a new String(bytes) yourself. Or you could drop that library and use a different Base64 encoder, for example this one.

Some Google tooling such as GWT has an embedded version of commons-codec with a pre-1.4 Base64 class. You may need to make such tooling JARs inaccessible to your code by refactoring your project such that only the parts of your code that need that tooling can see the dependency.

@Adam Augusta is right, One more thing

Apache-HTTP client jars also comes in same category as some google-apis.

org.apache.httpcomponents.httpclient_4.2.jar and commons-codec-1.4.jar both on classpath, This is very possible that you will get this problem.

This prove to all jars which are using early version of common-codec internally and at the same time someone using common-codec explicitly on classpath too.