Language
Starting from this, the first thing we usually allude to is our language, which, although we generically call it Spanish, is Castilian (from the region of Castile).
Food and Music
No one can deny the influence of Spanish cuisine in America (and vice versa), our common use of olives, raisins, and capers in many of the dishes, the predilection for fried things, and the enormous similarity that exists, for example, between the hallacas stew in Venezuela, which are eaten only at Christmas (tamales in other countries), with the stews and casseroles of Castile, Asturias or Galicia, also typical of winter. The "golden century" of Spanish cuisine was forged in times of colonial miscegenation, which was racial, but above all it was cultural. And when the territories were separated, both inherited it.
Names and Surnames
Tell me a name of a Spanish city and I will look for its homonym in Latin America: Valencia, Merida, Barcelona, Puerto la Cruz, are cities in Spain, but also in Venezuela, as are names like Avila or Altamira; Cartagena, Medellin, Pamplona are cities in Colombia and Spain; as are Cuenca, Loja, Cordoba, Leon, Salamanca, Guadalajara in Ecuador, Mexico and Argentina; or the common name for the apostle in Santiago de Cuba, Santiago de Chile, Santiago de Leon de Caracas, which have their analogous with Santiago de Compostela in Spain.
Likewise, surnames such as González, García, Pérez, Martínez, Rodríguez or Sánchez, head the list of the most common in all Latin American countries, as well as in the Iberian country.
Religiosity
Almost all Western culture arrives in Latin America (or Hispano-America, I prefer to call it) through Spain. Philosophy, arts, literature, and religion, although they have a common Latin base, we have assumed them with Spanish nuances. An example is a deep devotion to the saints and the different invocations of the Virgin Mary, the paraphernalia and drama of the Holy Week celebrations, and the tolerance towards monotheistic religions such as Judaism or Islam.