The cube attack was proposed at the 2009 Eurocrypt. The attack derives linear polynomials for specific output bits of a BlackBox cipher. Cube attacks target recovery keys or secret states. In this paper, we present a cube attack on a 5-round Sycon permutation and a 6-round Sycon permutation with a 320-bit state, whose rate occupies 96 bits, and whose capacity is 224 bits. We found cube variables related to a superpoly with a secret state. Within the cube variables, we recovered 32 bits of the secret state. The target algorithm was Sycon with 5-round and 6-round versions of permutation. For the 5-round Sycon, we found a cube variable and recovered a state with a total of 2192 Sycon computations and 237 bits of memory. For the 6-round Sycon, we found cube variables and recovered a state with a total of 2192 Sycon computations and 270 bits of memory. When using brute force in a 5-round attack, 2224 operations were required, but the cube attack proposed in this paper had 248 offline operations, and 232 operations were required. When using brute force in a 6-round attack, 2224 operations were required, but the cube attack proposed in this paper required 295 offline operations, and 263 operations were required. For both attacks, offline could be used continuously after performing only once. To the best of our knowledge, this is the first cube attack on Sycon.