Is knowing the distribution of input domain only way to do cipher text only attacks?

Imagine there is a $n$ bit block cipher. The attacker has harvested some how all possible $2^n$ cipher texts for some given key. Without the knowledge of the distribution of input domain as in frequency counts or some statistical information of input data. Is it possible to perform ciphertext-only attacks? Are there any examples?

Edit: Stated in other way, what does it take to launch ciphertext-only attacks on block ciphers? Can you provide any examples?

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In what kind of attacks are you interested in: Anything that distinguishes the ciphertext (or is it the plaintext) from random? Or something more practical? – fgrieu Feb 1 '14 at 7:09
either way would be of help . – sashank Feb 1 '14 at 14:24

Since for any fixed key the encryption algorithm is a bijection from the set of $n$-bit strings onto itself, the set of all possible ciphertexts is regardless of the key and algorithm always the set of all $n$-bit strings and does not provide any information.