<p>I've got a message contained in an byte[], encrypted with "RSA/ECB/PKCS1Padding". To decrypt it I create a Cipher c and initiate it with</p>

<pre><code>c = Cipher.getInstance("RSA/ECB/PKCS1Padding");
</code></pre>

<p>Untill now I have only decrypted small messages, using the <em>doFinal()</em> method, returning an byte[] with the decrypted bytes. </p>

<pre><code>c.init(Cipher.DECRYPT_MODE, privateKey);
byte[] decryptetBytes = c.doFinal(encryptedBytes);
</code></pre>

<p>But in this case the data is bigger (approx 500 Bytes), and the <em>doFinal()</em>-method throws an exception (javax.crypto.IllegalBlockSizeException: Data must not be longer than 128 bytes). I guess I need to use the <em>update()</em>- method, but I can't figure out how to get it to work properly. How is this done?</p>

With RSA you can only encrypt/decrypt block with size up to your key length minus padding length. If you have data longer than your key maybe it is just merged in one array so you should split it into chunks with size of your key (128 bytes suggests 1024 key with no padding, I'm not sure if it's possible). Using update() is not the case here.
Simply, you have to know how this array was created.
Generally speaking, RSA shouldn't be used to encrypt large amount of data as it's quite time consuming. Should be used to encrypt key to symmetric cipher, like AES.
Take a look here:
https://www.owasp.org/index.php/Digital_Signature_Implementation_in_Java