No, it doesn't.
Hereditary cancer is rare; fewer than 10% of all cancer cases are hereditary. Cancer diagnosed after the age of 50 is even less likely to be hereditary.
If your mother's breast cancer was due to one of the 2 faulty BRCA genes known to be responsible for hereditary breast cancer, then you and your siblings have a 50% chance of inheriting that gene. But only 5 - 10% of all breast cancer cases are due to a BRCA gene, and if your mother's was one of the 90-95% that are not, then you are at no known increased risk of breast cancer.
You don't inherit a general tendency to get cancer, and there's no general 'cancer gene'.
A sign that a cancer MIGHT (only might) be hereditary within a family is when several members of the same side of that family have had the SAME type of cancer, especially if some developed it at a younger than usual age.
With at least one in three people getting cancer at some point in their lives, it's not unusual for several members of the same extended or even immediate family to have non-hereditary cancers.
Often people think this means cancer 'runs in their family', but this is rarely the case.
Both my parents had cancer too, and my mother died of it So did two of my grandparents, my aunt, my uncle and my cousin. Another cousin has recently been diagnosed.
None of their cancers were hereditary, and no members of my immediate or extended family have ever been considered at increased risk of any of the cancers they had.
Of my parents' 6 children, now aged from 50 to early 60s, I am the only one who has developed cancer, and mine too was non-hereditary and unconnected to theirs
EDIT: I notice someone has said ''Of course other cancers are hereditary like breast cancer.'' Breast cancer is no more likely to be hereditary than any other type of cancer. As I've pointed out already, only 5 - 10% of breast cancer cases have a hereditary factor