MIDI can be a pain sometimes.
OK, recording first. First thing you need to do is make sure that you've got MIDI coming out of the SR16 when you hit the pads. If there is a way to enable/disable the MIDI output in the SR16 (which I'm not familiar with), make sure it's enabled. Find out what MIDI channel it's sending on. It may be channel 10, which is common for drums. But any channel is OK.
It's helpful if you can
confirm that the SR16 is actually outputting MIDI. One way to do this is with another keyboard or sound module if you have one. Plug the MIDI output of the drum machine into the MIDI input of the sound module. Set up the sound module to receive MIDI on the same channel that the SR16 is sending MIDI. Play the SR16 pads and see if you hear any notes playing from the module. If you don't have another sound module, that's OK. You can skip this paragraph. Sometimes it's helpful to take the computer completely out of the picture to confirm that your are sending MIDI.
OK, now on to recording into the computer. Plug the SR16 MIDI output back into the SBLive MIDI input. (The adapter you have should be fine.) Go into the "Setup MME" program and make sure that the SBLive is listed under MME inputs. It should not say "Inactive:" before the SBLive name. If it does, press "Set active" to activate it. Close the program and open up Cubasis.
Go to the Options menu and open up the MIDI System Setup dialog box. You should see a dropdown list called "Input From". Look in this list and make sure SBLive is listed that and make sure it is enabled. It is enabled if it has a checkmark next to it. If it doesn't, click on it to enable it. This tells Cubasis to listen to MIDI notes coming from the SBLive. For other settings in this dialog box, you can set MIDI thru as disabled. You should set "MIDI Input" and Mapped to" to the SBLive. Then exit this dialog.
Now play the pads on the SR16. Look at the MIDI indicator lights on the Cubasis transport bar. You should see the red input indicator light up when you play the pads. If you don't see this, then Cubasis is not seeing anything coming from the SR16. There is still a problem and you need to stop and figure out what it is. It doesn't matter what MIDI channel the SR16 is sending on; you should see the light as long as MIDI notes on any channel are being received by Cubasis. If you don't see the light, the problem could be either in the SR16 or the computer and it's hard to know which. (That's why it's helpful to use another sound module to confirm that the SR16 is at least sending MIDI notes. That would tell you that the computer is not setup correctly somehow.) Read the SR16 manual and do what you can to make sure it's setup correctly to output MIDI. One thing you can try is to loop the MIDI output of the SR16 back into it's input. Then when you play sounds on the pads they should sound doubled, or phased, because each sound is playing twice with the second one being slightly delayed. I guess the cymbals would be the easiest sound with which to hear this.
If you tried all this and still can't get the Cubasis MIDI indicator to light up, post again. I'm not sure if I have any ideas left, though.
Output
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You didn't say whether you got the output to work correctly. But you did do the right thing. You should manually create some MIDI notes in a part and then play the part to see if it works. Set the output of the track to SBLive and set the channel to the same channel that the SBLive is set to receive. (This is probably channel 10 or maybe even 1. But you can try all of them.) You should see the green MIDI indicator light on the transport bar light up when notes are output. If you don't, then something in Cubasis is not setup correctly. If you do, then the problem is either with the SBLive, the MIDI cable connection, or the SR16 itself. Make sure that the notes you manually created actually correspond to drums in the SR16. Some notes may not correspond to any drum sounds.
Keep trying. If you have any general MIDI questions, remember you can also try posting those in the MIDI forum where you'll probably get a better response.
P.S. I am a computer programmer and I pretty much got started when I was 24, because it wasn't until then that computers were cheap enough that I could get my hands on one. Now I get deflated sometimes when I see 12 yr. olds writing programs, and also when I see programmers who started when they were 8 or 10 and have a much more natural facility for programming than I do.