I believe this palace is now the Palace of Pioneers. The building is a clubhouse for children to sing, dance and do artwork.
There are several photos available if one does a Google search under 'Images'.
I copied the info below from an Odessa website.
Vorontsovsky Dvorets (Vorontsov Palace) - Built in 1827 in classical Russian style, this palace was once the residence of Count Vorontsov, who served as Pushkin's guardian while the poet lived and worked (he was employed as a civil servant) here in exile. Pushkin considered Vorontsov to be a harsh chaperone and taskmaster, describing him as a "vandal, a cad, and a petty egoist," in letters to the writer Ivan Turgenev. The flamboyant Pushkin - known for his philandering - had an affair with Vorontsov's wife (perhaps history's most definitive case of "poetic justice"). Vorontsov was Governor of Novorossiisk (New Russia), a region that surrounded Odessa. His palace became the headquarters of the Odessa Soviet (a sort of city hall) after the Bolshevik Revolution, and later was restored to and became the Palace of Pioneers. Located at the far northeastern end of Primorsky Bulvar.