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The $n$-skeleton of the canonical cubulation $\cal C$ of $\mathbb{R}^{n+2}$into unit cubes is called the {\it canonical scaffolding} ${\cal{S}}$. In thispaper, we prove that any smooth, compact, closed, $n$-dimensional submanifoldof $\mathbb{R}^{n+2}$ with trivial normal bundle can be continuously isotopedby an ambient isotopy to a cubic submanifold contained in ${\cal{S}}$. Inparticular, any smooth knot $\mathbb{S}^{n}\hookrightarrow\mathbb{R}^{n+2}$ canbe continuously isotoped to a knot contained in ${\cal{S}}$.

Any smooth knot $\mathbb{S}^{n}\hookrightarrow\mathbb{R}^{n+2}$ is  isotopic to a cubic knot contained in the canonical scaffolding of  $\mathbb{R}^{n+2}$