The Bible does not say that "Mizraim" is what we call "Egypt" or that "Aram" is what we
call "Syria". ...
This is a strange statement. "Mizraim" is simply the Hebrew word for
Egypt, used repeatedly for the land of the Nile and the Pharaohs which
is what we call "Egypt". "Aram" is the Hebrew word transliterated in
some English versions and translated "Syria" in others, which refers to
a rather ill-defined territory roughly comparable to the modern state of
Syria and of which Damascus was for some time the capital. So I don't
know what you mean here. Because the Bible is not a dictionary it does
not explicitly tell us which Hebrew words correspond to which English
ones. But it provides enough geographical information to make these
identifications completely certain.
As for Kush, the biblical information may not be quite so certain, but
Ezekiel 29:10 seems to put the border of Kush at Aswan, strongly
suggesting that at least here Kush refers to Nubia.