Can I use standard electrical cable from a waterproof junction box when replacing an exterior light
"Normal" 3-core electrical cable has a name, NM or informally, Romex.  It is not listed for outdoor locations.  For that, you would use its brother, UF.

However, if it is all-conduit between the two junction boxes, it is not illegal to use cable, just a major pain.   The more practical choice is THWN-2 or XHHW,  which is individual wires and easier to work with.  Most hardware stores sell it by the foot.  With this wire, there is an indoor and outdoor classification, but generally only one kind of wire is sold, and it is dual rated.