A fuzzy logical algebra has diverse applications in various domains such as engineering, economics, environment, medicine, and so on. However, the existing techniques in algebra do not apply to delta-algebra. Therefore, the purpose of this paper was to investigate new types of cubic soft algebras and study their applications, the representation of cubic soft sets with δ-algebras, and new types of cubic soft algebras, such as cubic soft δ-subalgebra based on the parameter λ (λ-CSδ-SA) and cubic soft δ-subalgebra (CSδ-SA) over η. This study explains why the P-union is not really a soft cubic δ-subalgebra of two soft cubic δ-subalgebras. We also reveal that any R/P-cubic soft subsets of (CSδ-SA) is not necessarily (CSδ-SA). Furthermore, we present the required conditions to prove that the R-union of two members is (CSδ-SA) if each one of them is (CSδ-SA). To illustrate our assumptions, the proposed (CSδ-SA) is applied to study the effectiveness of medications for COVID-19 using the python program.