The problem isn't only that your brother is not paying the bills for something he benefits from and your mother doesn't. The problem is that he is taking advantage of
your mother, and your family. It meets the definition of financial abuse. The real question is what you can do about it, and legally, you do have a choice.
If your mother, at age 90, does not have a durable power of attorney (for finances), she needs one. If she is mentally competent to make this decision, I urge you and your siblings, except for your brother, to meet with your mother and explain the need for this document. It must be notarized. The "do it yourself" variety is better than nothing, but it is prudent to seek the advice of an elder law attorney to be sure the document you use complies with the law and permits your mother's "agent" on the power of attorney document to act on her behalf concerning all financial matters.
If your mother already has a durable power of attorney document, properly signed and notarized, the agent (I hope it's not your brother!)can shut off the cable. This will have to be done in writing, with a clear letter explaining the problem, that your mother did not make this decision, that your brother is taking financial advantage of her, and that her legal agent, her power of attorney, wants it stopped. You will need to provide a copy of the durable power of attorney document to the cable company, with the letter.
If that, for any reason, does not work, I recommend that you seek the advice of an attorney, who can be an advocate for your mother with the cable company. This must stop and your family must stop allowing your brother to take advantage of your mother and you, who have paid the bills. The law is there to help you, and to protect your mother from financial abuse. Please use it.
Other than that, it sounds as if you have an issue with your brother about his not helping out with chores for your mother. A family meeting is in order. Not talking about it will only lead to more of same, plus resentment. Please seek some outside help if you are unable to have that family meeting and work this out among yourselves. A written agreement as to how it's going to be is ideal. Some elder law attorneys are able to conduct such family meetings. Otherwise, a social worker from a social service agency serving elders, a geriatric care manager, or a professional mediator are good choices for the kind of help you may need.