Pensieve header: Chessboards.

ArrayPlot[
Table[Mod[i+j,2], {i,8}, {j,8}],
ColorRules -> {0-> White, 1->Black}
]

ArrayPlot[
Table[Mod[i+j,3], {i,8}, {j,8}],
ColorRules -> {0-> Red, 1->Green, 2->Blue}
]

{ArrayPlot[
Table[Mod[i+j,3], {i,8}, {j,8}],
ColorRules -> {0-> Red, 1->Green, 2->Blue}
],
ArrayPlot[
Table[Mod[i-j,3], {i,8}, {j,8}],
ColorRules -> {0-> Red, 1->Green, 2->Blue}
]}

Graphics3D[Table[
Cuboid[{2i,2j,2k}],
{i,0,4}, {j,0,4}, {k,0,4}
]]

Graphics3D[Table[
If[Mod[i+j+k,2]≠0,{},
Table[Cuboid[{2i+ii,2j+jj,2k+kk}],
{ii,0,1}, {jj,0,1}, {kk,0,1}]],
{i,0,4}, {j,0,4}, {k,0,4}
]]