Here's a trick you can try. It worked for me in an older version of Logic, and there's no reason it shouldn't work on anything else.

Turn local control off on your synth. If the tempo on your synth is at least close to that on your sequencer, just hit record on the sequencer and trigger the arp. The arp [b]should[b] print what it's playing. once that's done you don't really need the arp on anymore.

Now I have to experiment with this. Let me know if that works, otherwise, I'm going to my studio tomorrow and I'll be testing things out.

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Konichiwa, Bitches!.

option1: (lazy/ghetto way)

Set the tempo on the synth the same

Option 2:
Set cubase as master tempo, then set your synth to sync to external midi/clock.

option 3: set your synth as master tempo, and make cubase sync to external/midi clock/mtc. This is the easiest way as there is a dedicated button in the arrangement window to lock it/unlock it

TDG is right that on some synths the arp is sent over midi and is therefore recordable - this isnt the case for all though.
The CS1x for example doesnt send out the arp over midi- but the Cs2x does.
The advantage of doing this way is you can edit the arp and note pattern as you would any part- you arent restricted to the preset patterns