Código:

void clearCache() {

    if (mClearCacheObserver == null) {
        mClearCacheObserver = new CachePackageDataObserver();
    }

    PackageManager mPM = getPackageManager();

    @SuppressWarnings("rawtypes")
    final Class[] classes = {Long.TYPE, IPackageDataObserver.class};

    Long localLong = Long.valueOf(CACHE_APP);


    try {
        Method localMethod =
                mPM.getClass().getMethod("freeStorageAndNotify", classes);

        localMethod.setAccessible(true);
        // Start of inner try-catch block

        try {
            localMethod.invoke(mPM, localLong, mClearCacheObserver);

        } catch (IllegalArgumentException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        } catch (IllegalAccessException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        } catch (InvocationTargetException e) {
            // TODO Auto-generated catch block
            e.getCause().printStackTrace();
        }

        // End of inner try-catch block

    } catch (NoSuchMethodException e1) {

        e1.printStackTrace();
    }

}

Logcat:

java.lang.SecurityException: Neither user 10206 nor current process has android.permission.CLEAR_APP_CACHE.
     at android.os.Parcel.readException(Parcel.java:1620)
     at android.os.Parcel.readException(Parcel.java:1573)
     at android.content.pm.IPackageManager$Stub$Proxy.freeStorageAndNotify(IPackageManager.java:5081)
     at android.app.ApplicationPackageManager.freeStorageAndNotify(ApplicationPackageManager.java:2500)
     at android.content.pm.PackageManager.freeStorageAndNotify(PackageManager.java:4710)
     at java.lang.reflect.Method.invoke(Native Method)
     at com.onexsoftech.clearcacheapp.MainActivity.clearCache(MainActivity.java:278)
     at com.onexsoftech.clearcacheapp.MainActivity.insertDummyContactWrapper1(MainActivity.java:495)
     at com.onexsoftech.clearcacheapp.MainActivity.insertDummyContact(MainActivity.java:472)