struct Quadrature{T}
    x::Vector{T}
    w::Vector{T}
end

function cubature(f::F, quadrature::Quadrature, B::NTuple{N}) where {F,N}
    (; x, w) = quadrature
    function _f(_ι)
        ι = Tuple(_ι)
        z = map((i, b) -> getindex(x, i) * b, ι, B)
        ω = prod(i -> getindex(w, i), ι)
        f(z) * ω
    end
    K = length(x)
    sum(_f, CartesianIndices(ntuple(_ -> K, Val(N)))) * prod(B)
end

Q = Quadrature(randn(10), randn(10)) # just a mockup

@code_warntype cubature(sum, Q, (1.0, 2.0))

@noinline prod_outside(w, ι) = prod(i -> getindex(w, i), ι)

function cubature(f::F, quadrature::Quadrature, B::NTuple{N}) where {F,N}
    (; x, w) = quadrature
    function _f(_ι)
        ι = Tuple(_ι)
        z = map((i, b) -> getindex(x, i) * b, ι, B)
        ω = prod_outside(w, ι)
        f(z) * ω
    end
    K = length(x)
    sum(_f, CartesianIndices(ntuple(_ -> K, Val(N))))
end