She performed with the Clark Terry Quintet and Big Band at Village Vanguard, Birdland, Blue Note, Queen Elizabeth 2, Royal Viking, S.S. Norway jazz cruises and clubs, concerts and festivals in the U.S, Europe, the Caribbean and South America. While working with the Clark Terry quintet she had the opportunity to perform with guest artists Al Grey, Red Holloway, Jimmy Heath, Frank Wess, Marian McPartland, Dianne Reeves, Joe Williams and Lou Donaldson to name a few.

Cuenca has also performed with such jazz luminaries as Billy Taylor, Frank Foster’s Loud Minority Big Band, Houston Person, Etta Jones, Helen Merrill, John Hicks, Valery Ponomarov, Lew Soloff, James Spaulding, Kenny Barron, Ray Drummond, Michael Brecker, Randy Brecker, George Cables, Hilton Ruiz, Jon Faddis, Eddie Henderson, John Handy, Kenny Drew Jr., Emily Remler, Richie Cole, Dave Stryker, Gregory Porter, Jessie Davis, Sean Jones, John Clayton, Ralph Bowen, Vincent Herring, Paul Bollenback, Geoffrey Keezer, Mark Whitfield, Ralph Moore, Paula West,  Catherine Russell, Dianne Reeves, Dianne Schuur, Denise Donatelli, Ernestine Anderson, Jazzmeia Horn, Lea Delaria, the European based Vienna Art Orchestra and many others. 
She was a guest clinician at the Sisters in Jazz Program at the IAJE Convention in NYC and the Mary Lou Williams Jazz Festival at the Kennedy Center in Washington D.C. Cuenca has been a longtime faculty member at the Jazz for Teens and Pre-Teen Program at NJPAC and the Stanford Jazz Workshop in California. Recently she has been on faculty at Roni Ben-Hur’s Summer Jazz Camp in Vermont.  She was an artist-in-residence at various universities in the U.S. and Europe with the Clark Terry quintet, Eddie Henderson quartet and as a leader with her own groups. In 2014 she received a B.A. degree in Jazz Performance from Empire State University in NYC.

In 1988 and 1991 Cuenca received jazz performance grants from the National Endowment for the Arts and in 1992 she was a semi-finalist in the Thelonious Monk International Drum Competition. In 2022 she received San Jose Jazz New Works grant.

She has studied with jazz master drummers Adam Nussbaum, Victor Lewis, Keith Copeland, and Brazilian drummer Portinho. Sylvia endorses Canopus Drums, Zildjian Cymbals, Vic Firth sticks and brushes, and Remo Drumheads.