What is your diet like? If it's too restrictive it's bound to cause cheating and binges. Your have to make sure it's a balanced diet. You can survive without sugar however you do have to have some protein and keep your blood sugar levels even in order to feel sane. Without knowing what your diet is its impossible to know if it's even appropriate to say "you can do it!" Because some diets can be ridiculous.
"Binging is a descent into a world where every restriction... is cut loose. At its core is a feeling of deprivation.. a feeling you can never get enough. Binges do not signify a lack of willpower or inability to care for yourself. On the contrary, binges are a urgent attempt to care for yourself when you feel uncared for. They are the voice of survival. Binges are the mark of the self that says, 'I am tired of feeling deprived, of being told I am wrong, that I am bad." - Geneen Roth