This paper presents a novel cryptanalysis method of DES (2-DES and 3-DES) using nature-inspired algorithms; namely Cuckoo Search Algorithm and Grey Wolf Optimization Algorithm. We have shown the loophole of 2-DES and 3-DES encryption systems and discovered the vulnerabilities by some simple mathematical calculations. The Meet-In-The-Middle approach can be executed on 2-DES along with Known Plaintext Attack, Chosen Plaintext Attack, and Chosen Ciphertext Attack. The valid key pairs along with the original key pairs can successfully be recovered by this attack algorithm. But in the Ciphertext Only Attack, the Meet-In-The-Middle approach fails to recover the plaintext as well as the valid key pairs both for 2-DES and 3-DES. To overcome this problem, we have proposed a novel cryptanalysis method of 3-DES with Ciphertext Only Attack using Cuckoo Search Algorithm and Grey Wolf Optimization Algorithm (GWO). We have developed a suitable fitness function, accelerating the algorithm toward the optimal solution. This paper shows how CSA and GWO can break a 3-DES cryptosystem using a Ciphertext Only Attack. This proposed cryptanalysis method can also be applied to any round of DES.