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The reliability measure of networks is of significant importance to the design and maintenance of networks. Based on connectivity, many refined quantitative indicators for the reliability of network systems have been introduced. The super vertex edge-connectivity and cyclic edge-connectivity, as important parameters to evaluate the robustness of networks, are explored extensively. As a variant of the hypercube <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Q</mi><mi>n</mi></msub></semantics></math></inline-formula>, the varietal hypercube <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><msub><mi>Q</mi><mi>n</mi></msub></mrow></semantics></math></inline-formula> has better properties than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Q</mi><mi>n</mi></msub></semantics></math></inline-formula> with the same number of edges and vertices. Wang and Xu have proved that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><msub><mi>Q</mi><mi>n</mi></msub></mrow></semantics></math></inline-formula> is super vertex-connected for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></semantics></math></inline-formula> and is also super edge-connected if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>≠</mo><mn>2</mn></mrow></semantics></math></inline-formula>. In this paper, we use another method to prove these results. Moreover, we also obtain the super restricted connectivity and the cyclic edge-connectivity of the varietal hypercube <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><msub><mi>Q</mi><mi>n</mi></msub></mrow></semantics></math></inline-formula>.