What kind of cucumber? No idea what our sand-sifting ones eats (just little pieces of whatever it finds), but our filter feeding cucumber appears to eat more after I feed Rods or add some phyto to the tank. It's a little hard to tell because she filter feeds nearly every night, but after I feed those foods I'm fairly certain I see her putting her feeders into her mouth more frequently.
The two staples I feed are Rods and PE Mysis. I figure the mysis makes up the bulk of the diet of most fish in the tank, and the Rods adds variety and covers the smaller critters. Though I am a firm believer in variety (just because we don't know exactly what our critters need for optimum health), so I also feed roe, cyclopeeze, reef chili and phyto (sparingly), and NLS pellets (which none of my current fish particularly care for, unless I soak them in Rods to disguise them).