Well....your male sounds like he is still very much in his kitten phase. My male and female cats both sleep with me (I shut them in my bedroom) but inevitably...my male is the one who wants to get out and explore at 6 AM.
Here is an article that may help you:
EXCESSIVE NOCTURNAL ACTIVITY IN CATS
Why does my cat seem to be most active at nights?
Some cats are active at night or awake and "raring to go" very early in the morning. Since many owners are out at work or school during the day the cat may spend the daytime hours in rest and relaxation, especially if it is the only pet in the household. The catâ€™s day then begins when the owner arrives home to provide the cat with feeding, play and social interaction. Typical complaints are cats that nibble or even attack the ownerâ€™s ears or toes in bed, walking across the sleeping owners, nighttime vocalization, or explosive, uncontrollable play sessions across the furniture and/or owners, during the night or early morning. Some owners inadvertently reward the behavior by giving the cat a little food, affection, or attention to try and calm the cat.
How can I stop my cat from keeping me up at night?
You must learn to schedule and encourage play and feeding during the daytime and evening hours, so that the catâ€™s schedule more closely matches that of yourself.
Some cats can be retrained by keeping the cat awake and active by playing, feeding and interacting with the cat throughout the afternoon and evening. Catnaps in the evening should be discouraged.
If the cat continues to disturb you during the night, confining your cat out of the bedroom, and providing it with a comfortable sleeping area and litter may do the trick. Do not provide food through the night as this encourages the cat to stay awake. On the other hand, if the cat remains awake, providing the cat with ample opportunity for scratching, climbing and play in a confined area may occupy the cat until it becomes tired.
Cats that are vocal when locked out of the bedroom must be ignored. Going to the cat or giving attention in any way will only serve to reward the demanding behavior. Cats that scratch or bat at the bedroom door can be kept away by the use of an upside down carpet runner, electronic pet mat or perhaps a motion detector (although it might disturb the owner). If the cat is overly vocal, lock it away in as sound proof an area as possible such as a washroom, or a cat carrier in a distant bedroom. Nested corrugated cardboard boxes around the cage help to further reduce the noise.
What if it is necessary to have the cat sleep in the bedroom?
If you decide that your cat would do best if allowed to stay in the bedroom, you must remember that any attention whatsoever will further reinforce the behavior. React to the demanding cat with inattention. However if the cat persists or the behavior escalates to a point where it cannot be ignored, punishment may be effective.
It should first be noted that punishment is generally contraindicated in cats because punishment that is too mild is likely to be ineffective and may actually serve to provide enough play or attention to reward the behavior. Punishment that is too harsh on the other hand could lead to an increase in anxiety, fear of the owner and even aggression. If punishment is to be used, devices that quickly deter the cat without the need for owner contact, such as a water sprayer, air horn, ultrasonic device or compressed air are usually the safest and most effective.
Is there medication that might help?
If all else fails and the cat does not sleep through the night with behavioral techniques alone, your veterinarian may be able to provide some medication to help your cat fall asleep for the first few nights.http://www.askdrpetra.com/Cats/Exces...20Activity.htm