DownloadNuGetPackage.cs

using NuGet.Common;
using NuGet.Configuration;
using NuGet.Frameworks;
using NuGet.Packaging;
using NuGet.Packaging.Core;
using NuGet.Packaging.Signing;
using NuGet.Protocol;
using NuGet.Protocol.Core.Types;
using NuGet.Resolver;
using NuGet.Versioning;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Threading;
using System.Threading.Tasks;

namespace ConsoleApp5
{
    class Program
    {
        static async Task Main(string[] args)
        {
            var packageId = "cake.nuget";
            var packageVersion = NuGetVersion.Parse("0.30.0");
            var nuGetFramework = NuGetFramework.ParseFolder("net46");
            var settings = Settings.LoadDefaultSettings(root: null);
            var sourceRepositoryProvider = new SourceRepositoryProvider(settings, Repository.Provider.GetCoreV3());

            using (var cacheContext = new SourceCacheContext())
            {
                var repositories = sourceRepositoryProvider.GetRepositories();
                var availablePackages = new HashSet<SourcePackageDependencyInfo>(PackageIdentityComparer.Default);
                await GetPackageDependencies(
                    new PackageIdentity(packageId, packageVersion),
                    nuGetFramework, cacheContext, NullLogger.Instance, repositories, availablePackages);

                var resolverContext = new PackageResolverContext(
                    DependencyBehavior.Lowest,
                    new[] { packageId },
                    Enumerable.Empty<string>(),
                    Enumerable.Empty<PackageReference>(),
                    Enumerable.Empty<PackageIdentity>(),
                    availablePackages,
                    sourceRepositoryProvider.GetRepositories().Select(s => s.PackageSource),
                    NullLogger.Instance);

                var resolver = new PackageResolver();
                var packagesToInstall = resolver.Resolve(resolverContext, CancellationToken.None)
                    .Select(p => availablePackages.Single(x => PackageIdentityComparer.Default.Equals(x, p)));
                var packagePathResolver = new PackagePathResolver(Path.GetFullPath("packages"));
                var packageExtractionContext = new PackageExtractionContext(
                    PackageSaveMode.Defaultv3,
                    XmlDocFileSaveMode.None,
                    NullLogger.Instance,
                    new PackageSignatureVerifier(
                        SignatureVerificationProviderFactory.GetSignatureVerificationProviders()),
                    SignedPackageVerifierSettings.GetDefault());
                var frameworkReducer = new FrameworkReducer();

                foreach (var packageToInstall in packagesToInstall)
                {
                    PackageReaderBase packageReader;
                    var installedPath = packagePathResolver.GetInstalledPath(packageToInstall);
                    if (installedPath == null)
                    {
                        var downloadResource = await packageToInstall.Source.GetResourceAsync<DownloadResource>(CancellationToken.None);
                        var downloadResult = await downloadResource.GetDownloadResourceResultAsync(
                            packageToInstall,
                            new PackageDownloadContext(cacheContext),
                            SettingsUtility.GetGlobalPackagesFolder(settings),
                            NullLogger.Instance, CancellationToken.None);

                        await PackageExtractor.ExtractPackageAsync(
                            downloadResult.PackageSource,
                            downloadResult.PackageStream,
                            packagePathResolver,
                            packageExtractionContext,
                            CancellationToken.None);

                        packageReader = downloadResult.PackageReader;
                    }
                    else
                    {
                        packageReader = new PackageFolderReader(installedPath);
                    }

                    var libItems = packageReader.GetLibItems();
                    var nearest = frameworkReducer.GetNearest(nuGetFramework, libItems.Select(x => x.TargetFramework));
                    Console.WriteLine(string.Join("\n", libItems
                        .Where(x => x.TargetFramework.Equals(nearest))
                        .SelectMany(x => x.Items)));

                    var frameworkItems = packageReader.GetFrameworkItems();
                    nearest = frameworkReducer.GetNearest(nuGetFramework, frameworkItems.Select(x => x.TargetFramework));
                    Console.WriteLine(string.Join("\n", frameworkItems
                        .Where(x => x.TargetFramework.Equals(nearest))
                        .SelectMany(x => x.Items)));
                }
            }

            async Task GetPackageDependencies(PackageIdentity package,
                NuGetFramework framework,
                SourceCacheContext cacheContext,
                ILogger logger,
                IEnumerable<SourceRepository> repositories,
                ISet<SourcePackageDependencyInfo> availablePackages)
            {
                if (availablePackages.Contains(package)) return;

                foreach (var sourceRepository in repositories)
                {
                    var dependencyInfoResource = await sourceRepository.GetResourceAsync<DependencyInfoResource>();
                    var dependencyInfo = await dependencyInfoResource.ResolvePackage(
                        package, framework, cacheContext, logger, CancellationToken.None);

                    if (dependencyInfo == null) continue;

                    availablePackages.Add(dependencyInfo);
                    foreach (var dependency in dependencyInfo.Dependencies)
                    {
                        await GetPackageDependencies(
                            new PackageIdentity(dependency.Id, dependency.VersionRange.MinVersion),
                            framework, cacheContext, logger, repositories, availablePackages);
                    }
                }
            }
        }
    }
}

I had to update/change this line replacing PackageSignatureVerifier to ClientPolicyContext:

var cliCtx = ClientPolicyContext.GetClientPolicy(NullSettings.Instance, NullLogger.Instance);
var packageExtractionContext = new PackageExtractionContext(PackageSaveMode.Defaultv3,
                                            XmlDocFileSaveMode.None,
                                            cliCtx,
                                            NullLogger.Instance);

I presume the version of the packages I am using (6.9.1) is newer than when you wrote this?