It is honestly cadet-dependent. I know cadets who sleep from 2300-0630. Some sleep from 0100-0630, and depending on the efficacy of your time management skills, some cadets end up not sleeping at all for a day or so (all-nighter to complete assignments).
There are 4 different types of weekends at the academy:
B (base, so the whole weekend is yours),
F (football; game usually on Saturday, but kind of turns into a B weekend after the game is over)
A/C (Commandant's training; some type of military development from early Saturday morning till about noon)
A/D (Dean's weekend; the focus is on academics, could be like a B weekend if you opt not to do any work, but I don't suggest this)
On B weekends, you can sleep as much as you'd like. On F weekends, you'll probably be up early Saturday morning to prepare for a football game, then you can nap afterward. A/C training typically ends before noon, so you can sleep as much after that, but you'll still be up pretty early to jumpstart the training. A/D weekends you can sleep as much as you'd like also. Of course, Sunday you can sleep how much you desire as well, but there will be a recall formation in the evening for accountability purposes. Sometimes this recall formation may be on a Monday due to a 3-day weekend.
For summer training, your amount of sleep will depend on the detail (CBT, CFT, CLDT, etc.) that you participate in. For beast, I remember going to bed around 2330 and waking up 0530-0600. Keep in mind that your cadre is always one step ahead of you, so they go to bed later than you and wake up earlier than you. For CFT, I went to sleep whenever I wanted, but I still had to wake up around 0600 to PT. You will PT almost every day during your summer detail. Concerning MIADs (Air Assault, Airborne, Sapper, etc.), I can't offer much perspective there. I haven't gone to any of those schools.
So obviously this is a rather expanded response to your initial question, but just to be concise, I would guesstimate that on average, cadets tend to get between 5-8 hours of sleep throughout the academic year and summer training. Weekends are slightly more difficult to predict, but perhaps an average of 7-10 hours for them.
Hope this helps. Let me know if you have any other questions!