Hume argued that assuming A causes B isn't the same as arriving at a truth of logic. However, even though Hume cautioned the "the mental habit" of induction should be used carefully he still believed it could be useful and didn't deny causation outright. In other words, I can't conclude A causes B like I can say there are no round squares, but Hume denied such a thing as an uncaused cause and accepted that things are causally determined. Therefore I can say the sun will rise tomorrow if I correctly understand the causes of sunrises and that those causes occurred. Am I understanding this correctly?
The problem of induction is our tendency to project past observations onto current or future situations without the use of reason. We do it out of custom/habit, and because the inductive evidence is so strong we can rely on it for our daily lives.
Hume says you can say the sun will rise tomorrow simply because you have experiential knowledge of it rising, a posteriori. You do not need to know any related causes, only that this has occurred before, so you have reason to expect it to happen again.
Knowing the sun will rise tomorrow is not a cause/effect relationship outside of your own collected experiences. It's one of Hume's matters of fact formed from a habit of expectation and an association of your own ideas (day and night, the time on your clock, etc).
If you wanted to substantiate your claim that the sun will rise tomorrow, you could cite other causes, yes. They would not avoid the problem of induction, though, because they are still experiential in nature, which leads to circularity.
There are some pretty good responses in another SE thread about solving the problem of induction that go into more depth with non-Hume resources.
Main source: Hume's Enquiry Concerning Human Understanding, Sections 4 & 5
Hume denies the validity of the Principle of Sufficient Reason (PSR), and, as I see it, he effectively denies all cause and effect. In A Treatise of Human Nature, he considers several arguments in PSR’s support, including those from Thomas Hobbes and John Locke (THN, I, 3, 3). Although this principle is said to be “impossible for men in their hearts really to doubt”, Hume finds “no mark of any such intuitive certainty” (THN, I, 3, 3).
[A]s all distinct ideas are separable from each other, and as the ideas of cause and effect are evidently distinct, it will be easy for us to conceive any object to be non-existent this moment, and existent the next, without conjoining to it the distinct idea of a cause or productive principle. (THN, I, 3, 3)
It is hard to see what might be left of causation after such a statement. The idea that an object can exist one moment and be non-existent the next, without any reason, destroys any possibility of continuity, so long as there is some discontinuous result that may be conceived.
The point isn't 'solving' the problem of induction, it is recognising limits on the certainty of our knowledge. Arguably doing that, is one of the unique hallmarks of science. https://scienceornot.net/2012/02/07/all-scientific-models-are-tentative/
Quantum mechanics is a great illustration of this. Causality has been abandoned at a fundamental level, for a probability based pattern-like correlation. https://scienceornot.net/2012/02/07/all-scientific-models-are-tentative/
The pattern-based (rather than fundamental) nature of causality at a macro-scale has been obscured by the interlocking and cross-correlation of relatively complex macro-scale systems.