

$$V = {S}^3$$
Volume
$$S = \sqrt[3]{V}$$
Edge
$$D = S\sqrt{3}$$
Cube diagonal
$$S = \frac{D}{\sqrt{3}}$$
Edge
$$A_{base} = {S}^{2}$$
Base area
$$S = \sqrt{A_{base}}$$
Edge
$$d = S\sqrt{2}$$
Base diagonal
$$S = \frac{d}{\sqrt{2}}$$
Edge
Total surface
$$S_{tot} = A_{base} + 2S_{lat}$$
Total surface
$$S_{tot} = 6{S}^{2}$$
Total surface
$$S_{tot} = 6A_{base}$$
Total surface
$$S = \sqrt{\frac{S_{tot}}{6}}$$
Edge
$$S_{tot} = 2{D}^{2}$$
Total surface
$$D = \sqrt{\frac{S_{tot}}{2}}$$
Cube diagonal
Lateral surface
$$S_{lat} = S_{tot}  2A_{base}$$
Lateral surface
$$S_{lat} = 4{S}^{2}$$
Lateral surface
$$S = \sqrt{\frac{S_{lat}}{4}}$$
Edge
Cube inscribed into a sphere
$$R = \frac{\sqrt{3}}{2}S$$
Circumscribed radius
$$S = \frac{2}{\sqrt{3}}R$$
Edge
Cube circumscribed to a sphere
$$r = \frac{S}{2}$$
Inscribed radius
$$S = 2r$$
Edge
Radiuses relation
$$R = r\sqrt{3}$$
Circumscribed radius
$$r = \frac{R}{\sqrt{3}}$$
Inscribed radius
Definition
A cube, or regular hexahedron, is a polyhedron bounded by 6 square faces, 8 vertices and 12 edges.
Properties
 6 congruent square faces, perpendicular to two by two to each other
 A cube is a regular hexahedron. A hexahedron is any polyhedron with six faces
 All the Square formulas are valid
Data  Formula 

Volume  V = S^{3} 
Edge  S = ^{3}√(V) 
Cube diagonal  D = S√3 
Edge  S = D / (√3) 
Base area  A_{base} = S^{2} 
Edge  S = √(A_{base}) 
Base diagonal  d = S√2 
Edge  S = d / √2 
Total surface  S_{tot} = A_{base} + 2 × S_{lat} 
Total surface  S_{tot} = 6S^{2} 
Total surface  S_{tot} = 6 × A_{base} 
Edge  S = √(S_{tot} / 6) 
Total surface  S_{tot} = 2D^{2} 
Cube diagonal  D = √(S_{tot} / 2) 
Lateral surface  S_{lat} = S_{tot}  2 × A_{base} 
Lateral surface  S_{lat} = 4S^{2} 
Edge  S = √(S_{lat} / 4) 
Data  Formula 

Circumscribed radius  R = (√3/2) × S 
Edge  S = (2/√3) × R 
Data  Formula 

Inscribed radius  R = S/2 
Edge  S = 2r 
Data  Formula 

Circumscribed radius  R = r√3 
Inscribed radius  r = R/√3 